serious-discussion

[tough island]

if AI can do CS you can kiss everything else you love Goodbye

[static shuttle]

This is extremely not true in my opinion

when programmers invented code generation in the 80s or whatever, that didn't replace programmers, it just reduced boilerplate they had to write

AI in my experience (video game programming) is garbage at actually solving real issues that arise when trying to program to solve technical problems, in my experience it's just worse code generation (in terms of correctness, but a bit more versatile)

[primal seal]

Except, of course, if the subject of your work is human beings directly

Yeah I think it’s natural to deny the power of AI

[static shuttle]

I am personally scared of managers thinking (incorrectly!) that AI can replace programmers, but not at all scared that it can replace humans at the actual hard tasks that make hiring programmers worthwhile

[primal seal]

It is scary, soon most of us will be obsolete, but who knows when

[jagged forge]

exponential growth is exponential until it's not

[static shuttle]

The main problem I see is that the models are fundamentally limited when it comes to working with problems they haven't seen versions of before: they are essentially just plagiarizing their data set mixed with some inference

so sure it looks impressive if you stick in your CS 101 homework or doing the same CRUD boilerplate API a million times in a row

but give it a technical problem in a framework it hasn't seen before thousands of times and it's like asking a toddler but with less creativity and better grammar

[primal seal]

Yeah, but menial jobs have large numbers

[tough island]

Not denying AI, simply saying when it reaches this point everyone is cooked. Social work will simply be oversaturated

[static shuttle]

This was my experience - I was working on a proprietary game engine for a co-op job, and the company approved funding for some like AI tools to help the programmers (since AI that are NOT LLM based have made remarkable strides at improving workflows of professional animators) along the lines of copilot

and it was useless, it had no clue how to function in the engine even though its dataset included our entire codebase with millions of LOC from past games

[tough island]

The least of our problems when AI automates every job are jobs, you better figure out if your country can implement UBI or you arfe done

are

[wooden falcon]

Lol AI cannot do CS. And CS is not going to be obsolete anytime soon.

I got into CS because I consider it the most fascinating topic I’ve ever encountered. I love learning it and doing it. That’s all there is to it.

[static shuttle]

so like yeah it could write basic boilerplate, but so can Guice, and Guice will never make a mistake because it's a deterministic code generator

[primal seal]

Cannot yet

[wooden falcon]

deterministic code generators are great. Life savers and yeah it’s so nice to know they always work

[jagged forge]

[citation needed]

[wooden falcon]

Lol ok

If you want to be a doomer that’s your business

but just know it has little basis in reality

[primal seal]

I don’t see the harm in presenting the viewpoint

[jagged forge]

well, saying it with brazen confidence and no evidence is something

[primal seal]

I never speak like a sheep

[woven rapids]

is evidence being a sheep

[primal seal]

I don’t really understand where the call for evidence is coming from when we’re just speculating on the future

[woven rapids]

I think there needs to be evidence to state that a field isn’t worth going into

[primal seal]

Reread

I phrased it as a question

[woven rapids]

Doesn’t change your point

[jagged forge]

you phrased it like a question but you obviously have your mind made up....

[primal seal]

It’s a possible outcome in the space

Guys

Quit being soft

[jagged forge]

is that supposed to mean anything lmao

the evidence so far shows that AI scaling is slowing, and adoption is struggling

so i'm inclined to be skeptical of your claims, which by the way aren't substantiated by fact

[woven rapids]

girl acting like a republican grifter over this

[primal seal]

I think it’s more laughable that I presented a possibility that made you guys emotional

[woven rapids]

we aren’t emotional we just think it’s a bad idea to tell people to not go into a field due to theory with 0 evidence

[true zinc]

AI is cool, AI is useful, AI still can't solve my computation proofs

[primal seal]

I really didn’t tell anyone to do or not do anything.

[jagged forge]

you criticize us, and yet you still haven't provided anything substantive to the conversation....

[woven rapids]

this lol

[primal seal]

I merely provided a perspective that maybe you’re not ready to imagine yet. Will it play out, of course no one knows.

[woven rapids]

AI is bad at a lot of things

[woven rapids]

girl it’s not a special perspective AI doomerism is everywhere

[jagged forge]

if this is all you can say to the points made by everyone else, you have nothing to say

[true zinc]

AI is nice for when I'm a lazyass and I want it to write my super template-y boilerplate

[woven rapids]

A lot of AI sucks tbh, AI writing is boring, AI art is corporate

[true zinc]

but not for when I wanna do proofs, "advanced" (not rlly) maths, whatever

[timid bronze]

I love AI for ranting

I go to AI if i need to rant

It wont tell anyone, good friend

[fresh comet]

[coarse bridge]

what you're saying is the sheep take though lmao

it's repeated by every chronically online zoomer from here to timbuktu

[primal seal]

In sincerity, it is very heart warming listening to everyone

[tough island]

Discord quassi intellectual

[tough island]

Agreed

[jaunty ibex]

I think you are pretty pessimistic

You might need to change your views

[primal seal]

I think I have

You guys are very persuasive

Definitely AI won’t touch CS

[gritty crater]

If AI get to that point it can touch a lot of field not just CS

[primal seal]

Yeah, but it never will

[gritty crater]

Programming is just the lowest thing in CS so if it can write some code I am more than happy

[coarse bridge]

where have you actually made an argument for the stance youre taking?

[primal seal]

Why would I waste my time doing that?

[coarse bridge]

if you just basically repeated your claim over and over again, what even is there to refute

so dont cry about people being dismissive to you then

[primal seal]

I just wanted to air it

When did I cry?

[coarse bridge]

you started complaining about people asking for you to justify what you said and disagreeing with you

[primal seal]

Disagreeing is fine. But even if I have justifications, I have no obligations to state them

[coarse bridge]

ok then people have no obligations to take you seriously

[primal seal]

Still no disagreement

[coarse bridge]

ok my stance is that AI is gonna become all powerful and wipe out humanity in the next few months

[primal seal]

I acknowledge your opinion

Let’s wait and see

[nimble moss]

I welcome our AI overlords

[sturdy gulch]

i just got nitro
and now i realized holy shit

i dont know what emojis to use anymore

im cooked

[ocean harbor]

do you want suggestions

[old oak]

We can but hope

[fresh comet]

just train it on my mathcord messages

that ought to prevent such a scenario from taking place

[coarse bridge]

especially this one #chill message

[fresh comet]

[static loom]

.remindme 6months if @coarse bridge's fabled AI apocalypse has come to pass

[quasi jetty]

Created reminder if @coarse bridge's fabled AI apocalypse has come to pass (#serious-discussion message) for <t:1740463061:f>

[fresh comet]

For every set a, if for every set b for which b is an element of a, we have that there exists c such that c is an element of b and for every set d for which d is an element of a and there exists e such that e is an element of b and e is an element of d, we have that b equals d, then there exists a set f such that for every set g, if g is an element of a, then there exists h such that h is an element of g and h is an element of f, and for all i, if i is an element of g and i is an element of f, then i equals h.

[static loom]

so true

[old oak]

You didn't provide a perspective, you just said some things.

[static loom]

I wanna play what are we talking about

from skimming sounds like some kind of extrinsic vs intrinsic motivation thing goin on

"why do anything if someone/thing is better than me at it?" kinda vibes

[old oak]

Usually either becaue I enjoy it, or because I am paid to do so even though I'm not the best.

[coarse bridge]

$\forall$ a, $\forall$ b $\ni$ b $\in$ a $\implies \exists$ c $\ni$ c $\in$ b $\wedge$ $\forall$ d $\ni$ d $\in$ a $\wedge \exists$ e $\ni$ e $\in$ b $\wedge$ e $\in$ d, b = d, $\implies \exists$ f $\ni \forall$ g, g $\in$ a $\implies \exists$ h $\ni$ h $\in$ g $\wedge$ h $\in$ f $\wedge \forall$ i, i $\in$ g $\wedge$ i $\in$ f $\implies$ i=h

[fathom swallow]

chipotle

[coarse bridge]

that was not a good use of my time

[old oak]

Certainly not, especially beacuse there are errors

[coarse bridge]

yeah

[static loom]

learn how to do it with sed

[old oak]

Very sed

[coarse bridge]

i didn't even bother trying to make it coherent i just replaced the words with symbols

[fresh comet]

the original looked like this

[old oak]

I mean, sure, why not

[coarse bridge]

using $\ni$ for such that feels like a crime

[fathom swallow]

chipotle

[fresh comet]

it comes from this video (link takes you to the part where she read this out loud)
https://www.youtube.com/watch?v=7W92GX23zfA&t=1063s

[coarse bridge]

LMAO

[fresh comet]

that is where I got my paragraph from

the video is super well made though

unironically

[coarse bridge]

ill watch

[static loom]

$\forall a \left( \left( \forall b \left( b \in a \implies \exists c \left( c \in b \wedge \forall d \left( d \in a \wedge \exists e \left( e \in b \wedge e \in d \right) \implies b = d \right) \right) \right) \right) \implies \exists f \left( \forall g \left( g \in a \implies \exists h \left( h \in g \wedge h \in f \wedge \forall i \left( i \in g \wedge i \in f \implies i = h \right) \right) \right) \right) \right)$

[fathom swallow]

Merosity

[static loom]

if it's wrong ||blame chatgpt aint got time 4 dat. inb4 !nogpt||

[old oak]

Now give it to an LLM and see what the output is

[static loom]

presniped

[old oak]

Ah

[static loom]

[old oak]

Although I was more thinking of inputting that into ChatGPT and asking for an explaination of what it is

[static loom]

no idea

[jagged forge]

which one is it GPT, AC or zorn's lemma

[old oak]

What was the input?

[coarse bridge]

the statement of zorn's lemma is pretty nice sounding

[static loom]

https://chatgpt.com/share/ed7bb297-41f3-4af3-aaad-843387656316

[old oak]

It did correctly associate that statement with the AoC, although I'm almost sure this kind of formal version of the AoC is in the training data.

It's even on the Wikipedia page, albeit with different symbols

[jagged forge]

jesus i've never actually seen the axiom of choice stated formally

[coarse bridge]

yeah

lmfao

[fresh comet]

I liked the picture the video used

it actually makes the statement intelligible

[static loom]

AoC, Zorn's Lemma, and that third other way of saying it, are beyond my pay grade

[coarse bridge]

i think i first learned about it seriously in the proof of every vector space having a basis

before i just kind of had a vague idea

[jagged forge]

i first learned about it after my cs teacher cryptically said "the axiom of choice is true, the well-ordering theorem is false, and zorn's lemma is iffy"

[coarse bridge]

i saw this quote somewhere

[jagged forge]

yeah it's a famous quote

[coarse bridge]

A well-known joke alluding to this equivalency (which may defy human intuition) is attributed to Jerry Bona: "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" Zorn's lemma is also equivalent to the strong completeness theorem of first-order logic.

yeah

[static loom]

I remember either Gomez or Dami posting some annoying probability problem ending up using the well ordering of R

[jagged forge]

excuse me what the fuck

[static loom]

I can see how people would think the well ordering of R is false

[jagged forge]

i'm doing probability rn

if my textbook suggests to me to use the well ordering of R im quitting immediately

[static loom]

I think it was a problem specifically created to hinge upon picking stuff based on the well order of R or something

like uhh I forget this was years ago now

like you and someone else get to pick numbers from R or something

and because you're only picking countably many times

something idk

at this point it's probably enough information to build our own problem based on the idea somehow if we work at it

[old oak]

My preferred phrasing of that joke is "the axiom of choice is evidently true, the well-ordering theorem is evidently false, and who the hell knows with the Zorn Lemma"

Oh wait, Chipotle quoted that version above

[static loom]

Chipotle is owned by McDonalds

[quaint cipher]

what's this function

[static loom]

tangent probably

I'm pretty sure I've seen it written this way before

[fresh comet]

tan = tg in places like Russia, iirc

that's what my Russian hs math teacher told me, at least

[quaint cipher]

then what's this

[fresh comet]

cotangent

[coarse bridge]

i didn't know that

[fresh comet]

it's not common at all outside of a few areas

so that's not surprising

[coarse bridge]

yeah

makes sense

[old oak]

Yes, Poland as well. tg and ctg for tangent and cotangent (and arctg/arcctg for the inverse functions)

And ln for the natural logarithm is the prevailing standard, log tends to represent the decimal logarithm.

[fresh comet]

[old oak]

At least the Russian version of the CDF didn't get enough traction to cause confusion.

(they define (or used to define) the CDF of a random variable X as F(t) = P(X < t))

I.e. with strict rather than weak inequality, so all the continuity properties are reversed

[vast wraith]

i’ve seen tg used not infrequently in british articles from the first half of the 20th century

i think coxeter uses it

[old oak]

Also sec and cosec are basically nonexistent in high school trigonometry/university calculus courses

We get by with sin, cos, tan and cotan.

There's probably some specialist areas which do use sec and cosec, but the default curriculum doesn't even mention them.

[vivid halo]

log is standard for natural log once you get beyond high school math lol

[gritty crater]

In programming, log is also used to denote natural log

[old oak]

Not everywhere, is my point. In Polish ln is used to denote the natural logarithm even in advanced texts.

[glad pebble]

hello :3

[eternal crow]

Isn't it cosec and cotan

Bc i think sec and tan are pretty much used

[nimble moss]

it's just notation, I can define god(x)=sin(x) and it serves the same property

[cyan forum]

same in French

and many european countries

[nimble moss]

My math courses use log but physics use ln

dunno why tho

[cyan forum]

it all depends on context

[coarse bridge]

yeah i assume by default that log means natural log but i see both log and ln

i guess context usually makes it clear

[gritty crater]

That is why every time I see log without a base. It scares me out

[glad pebble]

am I allowed to ask in this server for math tutors? I couldn't find anything in the rules (unless I missed it) im really sorry if I'm not :((

[nimble moss]

I assume physics student probably don't know about natural log above highschool level in their earlier years and probably keeps using it later on

[eternal crow]

https://tenor.com/view/clouds-log-nosedive-downgrade-recession-gif-24200705

[gritty crater]

Wait, what I thought by default log mean log base 10

[glad pebble]

:3 (ill pay obvi)

[nimble moss]

Yeah in my highschool log means base 10 but in uni its natural log

[agile fiber]

in the natural sciences orders of magnitude & scientific notation are common, and log base 10 ties into that nicely

[cyan forum]

the reason why log is usually base 10 is because natural logarithm already has a notation ln, which is also a hommage to John Napier, and log base 10 is used a lot

[eternal crow]

Wolfram treats log as base e i think

,w log e

[fathom swallow]

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[agile fiber]

well log base e is more common in mathematical writings, but log base 10 is more common in science

[nimble moss]

its base 10 in desmos

[gritty crater]

Yeah, in engineering log often mean log base e not base 10

[cyan forum]

wolfram actually allows for both interpretations

[eternal crow]

I thought it's latin for logarithmus naturalis

[nimble moss]

ambiguity much?

[eternal crow]

Or smth like that

,w log 10

[fathom swallow]

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[eternal crow]

,w log(10)

[fathom swallow]

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[cyan forum]

anyways notations depend on a lot of stuff including context and regional stuff

like a lot of hispanic countries write sen instead of sin

there is no "correct" answer in general concerning notation

as long as your notation is defined properly, it is as valid as all others

[old oak]

With the exception of using ]a,b[ to denote the open interval

[gritty crater]

[cyan forum]

we will remember your ip address /j

[nimble moss]

They deserve to have tomatoes thrown at them

[agile fiber]

pros:

• parentheses are overloaded already
  cons:
• ugly

[cyan forum]

more pros : visual intuition

me when (a,b) actually refered to the interval instead of the R^2 vector:

[gritty crater]

(a, b) can mean a point, a vector, an interval

But vector often denoted by <a, b>, I think

[nimble moss]

That is even more cursed than ]a,b[

[gritty crater]

<a, b> is actually quite common, I think so

[eternal crow]

Would you use $\fallingdotseq$ instead of $\approx$

[fathom swallow]

0_א

[vast wraith]

this notation is ime more commonly used to denote the dot product between vectors a and b, ehehe

[nimble moss]

I like using a ket to denote a vector

,, |v\rangle

[fathom swallow]

Turquoise

[eternal crow]

,, \langle a,b\rangle

[fathom swallow]

0_א

[nimble moss]

beautiful looking

[vast wraith]

that said, in my norwegian high school introduction to vectors, we used the angle bracket notation to denote vectors

[agile fiber]

how to write a vector in \R[2]:
[ (x,y) ]
can be confused with a point (basically the same anyway) or an open interval
[ [x,y] ]
can be confused with a closed interval
[ \langle x, y \rangle ]
can be confused with an inner product
[ \begin{bmatrix} x \ y \end{bmatrix} ]
nobody wants to type all that
[ \begin{pmatrix} x \ y \end{pmatrix} ] nobody wants to type all that and it looks like a binomial coefficient
[ {x.y} ]
nobody actually does this

[fathom swallow]

cloud

[vast wraith]

in written notes i pretty much always use the column notation

and it’s pretty much arbitrary whether or not i use square brackets or parentheses

[gritty crater]

{x, y} can be confused with set

[coarse bridge]

ngl i haven't seen it denote base 10 since like middle/high school, but also they're comparing conventions in different countries and im only familiar with how its usually done in the US so

[agile fiber]

which is why nobody does it

[cyan forum]

i interpret this as the group/vector span of a,b

in case of vectors it's worse yeah can be seen as inner product

[agile fiber]

angle brackets seem to be mostly associated with calculus courses

[coarse bridge]

yeah lmao i had a prof who did this it doesn't sit well with me

i just write out the word span

[gritty crater]

So every notation for vector has a problem

[hot mauve]

Anyone could help me with a wuick trig in #geometry-and-trigonometry please

[cyan forum]

well in theory [x y]^T or (x y)^T

works completely fine

and overrides the "nobody wants to write all that" and "binom coefficient" problems

but that raises a question

[gritty crater]

[x y]^T looks fine to me as well just take space to write

[peak tide]

you can always invent your own funky brackets, like in loomis and sternberg:

[fathom swallow]

rafilou2003

[gritty crater]

I saw the word binom

[cyan forum]

easier to write that way

[nimble moss]

I was gonna say it's undefined but the \binom got me

[cyan forum]

imagine you didn't have access to the code xd

like now

and let people guess

[eternal crow]

I heard in compute science, log is base 2

[rocky shuttle]

\[\binom{20}{10}\]

[cyan forum]

when you're dealing with a bunch of 1s and 0s

[gritty crater]

Yeah, because in CS we deal with binary

[cyan forum]

{20}{10}

[eternal crow]

,,[\binom{20}{10}]

[fathom swallow]

0_א

᳄᳅᳆᳇

[rocky shuttle]

forgot how to use binom lmao

[eternal crow]

,,20\choose10

[fathom swallow]

0_א

[rocky shuttle]

anyways, this is the only option I don't get

[cyan forum]

like any respectable being vector * scalar

[rocky shuttle]

[gritty crater]

Wait waht

[eternal crow]

,, \frac{20!}{10!(20-10)!}

[fathom swallow]

0_א

[agile fiber]

one of them is a vector and the other is a binomial coefficient

[gritty crater]

Right

So the answer is in superposition?

[cyan forum]

one of those options is bigger than others

[eternal crow]

,w 20C10

[fathom swallow]

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[cyan forum]

omg I imagine a math olympiad like that so much
"Take 3 natural integers a < b < c. let n be the minimal integer such that c = binom(n,k) for some k > 0 and thus write c = binom(n,k). Then compute the vector X = binom(b,a) * [n k]^T. Write X = [x y]^T and compute m = binom(x,y). How many triples (a,b,c) verify a^3 + b^4 + c^5 = m?"

olympiad fever dream

[surreal sapphire]

whats the correct symbol for list concatenation?

im thinking || or ::

[old oak]

In Python it's +

[1,2] + [3,4] = [1,2,3,4]

I don't know if that's correct, but that's how it's implemented

But inconsistently, if you've got a numpy array instead of a list, + becomes pointwise addition:

Not great

[gritty crater]

Because numpy reimplements addition

But numpy often used for computing so it is quite convenient

You can rewrite addition for any object you created by rewriting __add__()

[surreal sapphire]

i mean correct in a moral sense

im writing an english text, not code

[old oak]

I know, and it's not really something that I suspect would cause me problems, I just observed the inconsistency

I agree that using + for pointwise addition in numpy makes more sense than for concatenation

[quaint cipher]

what's this notation?

[neat lintel]

Probably not divides

$q \nmid p$

[fathom swallow]

Bequi

[jaunty ibex]

Not dividing. As Bequi said

Number theory

[quaint cipher]

can we replace the [if] as [iff]

[proud olive]

yupp

it's basically the definition

[versed agate]

it seems to just be convention in definitions to use 'if'

not sure why

[quaint cipher]

but it actually can be iff?

[versed agate]

yeah, it's definitional

[quaint cipher]

Is the converse of this true? or is there any valid counterexample?

[versed agate]

The converse is not true, there are plenty of invertible discontinuous functions

[quaint cipher]

could u give some examples

[versed agate]

sure, take your favourite continuous monotone function on an interval and swap the images of the first and second halves

if you do it right, the image of the whole interval is still an interval

and the inverse will still exist

[lusty ether]

What are the applications of functions in life?

[solid snow]

like all of math

[lusty ether]

Well, then why do we need to learn complex plane geometry proofs? I don’t understand what the point of learning this is, it seems to have nothing to do with functions.

This is exam-oriented education

[river moon]

why does it need to be related to functions?

[lusty ether]

Don’t you know how to learn such complicated geometric proofs in your country?

[versed agate]

What level of maths are you at? Your role says postgrad

[lusty ether]

I'm just curious. If it doesn't matter, what's the point of learning this geometric proof? XD()

[lusty ether]

Advanced Mathematics Elementary Level

I can understand it, but I don't understand why it exists.

For example, if functions are very important, you can just learn algebra and simple geometry.

[river moon]

you're trying to say that somehow it is/isn't important to learn something just because it's not related to some other topic in math

I'd say the premise itself is wrong

[lusty ether]

yth

[versed agate]

pure mathematicians don't do maths in relation to other topics, but in relation to itself

[lusty ether]

so bro what is the significance of error learning?

[river moon]

"error learning"?

[versed agate]

often we'll find applications or explore something inspired by something else, but it's not necessary

[lusty ether]

Yes, because it doesn't matter.

[river moon]

what is error learning

[lusty ether]

I feel like there are too many branches of mathematics, but it's ridiculous to study the branches of mathematics.

[lusty ether]

Learning things that don't require any knowledge, such as spending 1-2 years learning geometric proofs, ∵∴, etc.

[versed agate]

"too many" by what metric?

[river moon]

but they do require some prerequisite knowledge

[lusty ether]

Well, I don't understand the point of doing this.

[river moon]

everything does

[versed agate]

certainly most won't interest most people

but sort of definitionally someone needs to have found something interesting for it to have been explored

[lusty ether]

Like algebra and geometry, its branches are complicated. I don't want to distinguish, but for non-geniuses, the indistinguishable categories are a headache.

[versed agate]

this mf denying the cogito

[lusty ether]

That's great, but it's a pity that some people are busy with life and can't learn the real things.

[versed agate]

if it helps, you can think of it more akin to an artistic or philosophical pursuit

[quaint cipher]

let's say x^3, wdym that swap the images of the first and second halves?

[versed agate]

so pick your interval, say [0, 1], and define f(x) = (x + 0.5)^3 for 0 ≤ x ≤ 0.5, and f(x) = (x - 0.5)^3 for 0.5 < x ≤ 1

[quaint cipher]

x^3 is monotone in R

[versed agate]

is R an interval by your definition? if it is I suppose you can pick any x at all to be your "midpoint"

0 might be conventional

[quaint cipher]

so swap it, we get -x^3, it's still monotone

[versed agate]

we translate the halves, not mirror them

over an unbounded domain it's a bit messy

but you can just chop and change smaller bits

[quaint cipher]

hmmm i dont understand how to do the translate?

say[-2,2], so first interval will be [-2,0], second will be [0,2]?

[neat lintel]

summation graphs are weird. why are they a bunch of short lines instead of just a bunch of points?

[solid snow]

what is a summation graph

[neat lintel]

a graph of a summation function

[solid snow]

which is…?

[versed agate]

Yeah, up to which interval 0 is in. We'll then add 2 to the first interval and take 2 away from the second before applying our monotone continuous function

[neat lintel]

say, E(200*0.98^n) from n=0 to x

[quaint cipher]

like this?

[neat lintel]

i can't draw symbols with text

[versed agate]

$$\sum_{n=0}^N{200 \cdot 0.98^n}$$

[fathom swallow]

robin goodfellow

[solid snow]

because the sum is only defined for integer x, desmos or whatever graphing software youre using is rounding non integer values of x and extending its domain

[neat lintel]

yea like that

[versed agate]

Using x as an upper bound for summation is a sin

[gritty crater]

Using that you can know what value does a sum approach

That is quite convenient, actually

[neat lintel]

why round it

[neat lintel]

i wanted to see what the value is depending on how many terms are there xd or if it ends up tapering off

[solid snow]

ask whoever programmed the graphing software

[neat lintel]

cus of the 0.98^n

[neat lintel]

aigh

[versed agate]

I don't have image privileges, but like {-2≤x≤0:(x+2)^3, 0<x≤2:(x-2)^3}

[neat lintel]

oh it does, at x=10000... thats crazy that it actually just stops there

[versed agate]

couldn't you just do a discrete limit?

[quaint cipher]

yes so it has inverse but not continuous, right?

[versed agate]

Exactly

nor monotone

[solid snow]

it does not

[quaint cipher]

this is kinda intuitively tho,-2≤x≤0:(x+2)^3, 0<x≤2:(x-2)^3 , is this a peicewise function?

[solid snow]

dont take whatever a graphing calculator shows as math truth

it has limitations and compromises to be able to display something

[versed agate]

yeah it's defined piecewise

[quaint cipher]

but both (x+2)^3 and (x-2)^3 have inverse right?

[gritty crater]

Graphing calculator has limitations

[versed agate]

yeah, any translation of an invertible function has an inverse

[quaint cipher]

impressive,ty

[versed agate]

all g

[neat lintel]

ive never properly dealt with summations before

never encountered them in school

[versed agate]

finite sums are pretty intuitive, but yeah be careful of infinite series

[neat lintel]

infinite series seem interesting

itd be nice to figure out which ones approach a certain value

[lusty ether]

Has anyone read the book "The Calculus Lifesaver"? Is it suitable for beginners to learn calculus?

Although it is for exams only, it seems a bit confusing.

[neat lintel]

i learned calc from 3b1b my goat

[lusty ether]

Oh my god, by watching the video

If 3b1b writes a book, it will be very interesting

[neat lintel]

i watched them on repeat a couple years before taking basic calc

[lusty ether]

Why do you need to watch it for so many years?

[neat lintel]

i didnt know what he was talking about

[lusty ether]

Well, maybe this is the only way to solve the problem

[neat lintel]

idk how or when i went from struggling to understand whats going on to "ahh yes ok now i will proceed to use calculus to help me solve problems outside school"

e

[lusty ether]

So, do you have any recommended books for beginners to learn calculus?

[versed agate]

Stewart is good for an introduction, and pretty universal

[lusty ether]

Okay, so what do you think of Thomas Calculus?

https://www.amazon.com/Thomas-Calculus-14th-Joel-Hass/dp/0134438981

Many people here give very good reviews, but I don't know which book to choose. I think they are all similar.

[versed agate]

I haven't read Thomas, maybe check #book-recommendations

[pearl hornet]

Guys I am currently reading apostols real analysis start to finish and was wondering if its bettter to finish the book before starting abstract algebra

At uni i have done abstract algebruh but only basic stuff since uni is not very in depth anymore at least in the uk

So my understanding is just from a few pages of lecture notes

Any very rigorous abstract algebruh books with good exposition?

[solar hawk]

lol algebruh

[pearl hornet]

Calclueless and algebruh

[kindred whale]

is there anyone that can help me understand limits from functions? i’m doing my assignment and from the videos i watch i understand the idea i just don’t get sometimes how let’s say ill try looking at the left side first, im not sure in which direction the function is moving

[ocean harbor]

New here? Welcome

See #❓how-to-get-help for this

And you can ping me if you want xd

[hallow furnace]

https://es.fiverr.com/s/pd0jLjp

[fresh comet]

<@&268886789983436800> promotion?

https://cdn.discordapp.com/attachments/1080555115066437686/1275095275140026459/1112374071854891058.gif

hey smay

[gusty socket]

thanks

what’s up higher

[fresh comet]

nothing much atm, how're you?

[gusty socket]

they have now been asked (different chat)

[gusty socket]

good i am computing stuff in local coordinates

[fresh comet]

just like your high school days

[gusty socket]

yeah, my high school days i wrote stuff down and barely understood it but i better get it this time around

[fresh comet]

sounds about right

[gusty socket]

considering i’ve had the last 5+ years to get better at mathematics

[fresh comet]

what the heck was I doing in my high school days (one year ago)?

[gusty socket]

though that isn’t always the best indicator of how much one’s actually improved LOL

[fresh comet]

I think I did literally no math outside of hmw back then

[gusty socket]

that’s fair enough

[fresh comet]

I really wish

I got into math earlier

[gusty socket]

why

it doesn’t matter so much

[fresh comet]

cause I would've enjoyed it no doubt

I just didn't know

[static shuttle]

fair, but you couldn't have really known

[fresh comet]

I'm not worried about the pace

[gusty socket]

but now you are doing it and enjoy it, who’s to say that you’ll continue to enjoy it in a few years? you’ll just enjoy it for however long you like it

maybe it’ll be forever

[bronze pelican]

Smay? More like smile 😃

[gusty socket]

hi yamin

[fresh comet]

true

[fresh comet]

hi yamin

how was your class?

[gusty socket]

omg yamin in class??

[bronze pelican]

It was ok

[fresh comet]

yamin is teaching one

[gusty socket]

very fun

[bronze pelican]

Did yesterday

[fresh comet]

ic

[static shuttle]

like expecting your past high schooler self to be super great at predicting the future and what you'll like with few hints towards it is super difficult

that was me post high school, I hated math and almost didn't go to uni

but through accidental string of stuff it happened and I realized I loved it

but I 100% would not have realized and had no way to realize it

[fresh comet]

I know, I'm not saying that I should've somehow had a crystal ball in front of me to predict the future

my remark was more melancholic

[static shuttle]

oh oh fair ic

mb

[fresh comet]

no, it's alright haha

[gusty socket]

wyd tonight higher

[fresh comet]

who knows

I live by the moment lmao

[gusty socket]

MAYBE i can actually come on and talk about stuff like i said i would do before :0

[fresh comet]

that would be cool

[gusty socket]

i have been bad about keeping the schedule but whatever

[fresh comet]

oh, there's a light novel series I wanna continue reading

that's maybe smth I'll do

what else uhhh

[gusty socket]

that’s good, after i’m done doing math i’ll continue reading the novel i started too

[fresh comet]

oh, there's another email I gotta write

I put off all my emails cause I hate doing it

[static shuttle]

the broken strategy

[fresh comet]

emails/applications are such a problem for me lmfao

I'm so lazy

[static shuttle]

is to force yourself to speedrun reply to them

and like don't proofread beyond like making sure you didn't insult their mother

[fresh comet]

[static shuttle]

unless it's like super duper important to be perfect about it

because then you reply to emails really fast and it's off the plate

[gusty socket]

HUGE btw, i loved doing this back when i was productive

[fresh comet]

I should maybe do that yeah

I tend to worry about the formatting of each sentence too much

makes me procrastinate a lot

[static shuttle]

yeah I'm like that in my writing

but for emails i realize people just skimread and read to get quick information

after seeing my advisor send great emails like

sounds good thanks

[fresh comet]

fair enough

[static shuttle]

sometimes ended with a -<name>

[fresh comet]

I've been putting off this one for 6 days now

I gotta force myself to go do it cause I can't wait forever

[static shuttle]

write it now!!!

[fresh comet]

you're right...

I'll go write

[pearl hornet]

Proofs moment

Real analysis is so fun ngl

Its a shame its so tiring writing the proofs tho

Not that it isnt fun

But proof writing takes much time to iron out the details

Especially when the book says "the proof is in the pudding" or some tomfoolery

So the progress is slow

[lilac umbra]

yaaaaas

[gusty socket]

put me in that class omg i love pudding

[junior veldt]

The proofs in real analysis definitely are interesting

You do have named theorems, but… honestly sometimes it feels like you more learn a collection of proof “techniques”

Where it’s more important to know how things are proved than to be able to recall the specific conditions for a theorem

That was at least my (admittedly limited) experience of it

[static shuttle]

I think the first bit of real analysis definitely is just building up the basics and developing the proof techniques, definitely feels like you get really important named theorems to apply later on?

[vast wraith]

statements i would never have imagined to read:

The odd numbers are not [socially] oppressed.

[static shuttle]

lol what's the context

[vast wraith]

gillian russel’s article, from anti-exceptionalism to feminist logic

[static shuttle]

is it some sociology thing? sounds interesting

[vast wraith]

very interesting read in the intersection logic and feminism

[agile fiber]

consider:

[static shuttle]

will check it out! thanks

[vast wraith]

whar

…is this a thing? i’ve never had a tv

[true zinc]

we relate to this too much, it must always be a multiple of 5, 10, or 11

[dim ocean]

hi guys, what’s the nicest and newest scientific calculator for math?

[true zinc]

Just use an online calculator at this point

unless you absolutely need a physical one

[bleak sapphire]

In which case look into physical graphing calculators

the kind that need proper batteries and have LED displays

otherwise go for a casio

like the one that has the complex numbers and the integral and derivative function

[earnest dove]

How to avoid perceived circularity when defining a formal language?

https://math.stackexchange.com/questions/173735/how-to-avoid-perceived-circularity-when-defining-a-formal-language

[bleak sapphire]

Uhh wheres the embed

I'd rather not click on any links that arent directly supported by discord

since I know theres some weird sneaky stuff one can do

[hidden dock]

does anyone know were freshman seminar is at ellet clc

all i know is thats its on third floor :/

[finite hare]

im also putting off sending an email for 9 months now

you write my email and I'll write yours @fresh comet

[fresh comet]

[burnt ledge]

HAHAHAHAHAHHAHAHAHAHHAHA

I love that theres 4 images saying thebsame thing

and theyre all from decades ago

[flint cliff]

Hi, does everyone know how to solve this kind of question. So you gotta fill up the underscore

10_19_4_5

with these operation:

a. +
b. -
c. :
d. ×
e. =

But each operation can only be used once. The number can't be swaped and no paratheses being used

For example:
10 - 19 = 4 + 5
But its wrong since -9 ≠ 9

[finite hare]

10 = 19 - 4 - 5

[hardy iron]

that's not a valid solution

[finite hare]

oh damn you're right

each operation can only be used once

my bad

[hardy iron]

There's no such combination

I tested it by bruteforcing in python

[finite hare]

yes I agree

[neat lintel]

yall said i shouldnt trust what the graphics calculator says about 1+0.98+0.98²+0.98³+... but i just solved it on my own and it seems to equal 10000

[indigo spindle]

what voodoo math are you doing

[neat lintel]

oh 200 times that infinite sum

asdf

200(1+0.98+0.98²+0.98³+...)

[flint cliff]

oh i see, thank you

[nimble moss]

That's a geometric series. Calculators can't do infinite sums, no?

[wooden falcon]

usually these sorts of problems are solved via brute force. It’s small enough that you can do that feasibly and easily (just tedious to code up).

[wild marsh]

Anyone mind quickly checking the answers in here

https://discord.com/channels/268882317391429632/1278902799047852042

[fresh comet]

ah, you're not supposed to advertise your help channel/thread in the discussion channels

or anywhere, actually

[neat lintel]

its not an infinite sum? there's an infinite number of terms being added up

if what they really wanted to tell me yesterday was that it's better to double-check what a calculator says, they should've been clearer about it

[brave hemlock]

just do
x = 1 + 0.98 + 0.98² + ...
x = 1 + 0.98(1 + 0.98 + 0.98² + ...) = 1 + 0.98x
and solve for x. If it converges this will give you correct answer

[autumn zenith]

sthu

[fresh comet]

huh?

[hardy iron]

There's an infinite number of terms being added up so it's an infinite sum

[sly jungle]

What's a good success rate on the exercises in Understanding analysis, Abbott? I'm on 70% for the first 2+ chapters and feel like it should be higher 😐

[nimble moss]

That's good imo

[gleaming adder]

if my book says "find a formula for ____" (as an exercise) am i supposed to prove it? understanding analysis too lmao

[nimble moss]

Context?

[static shuttle]

independently, that's a great success rate (better than me, and I learned half of my undergrad analysis from that book when I self-studied)! some of the exercises in that book are pretty hard, but provided you're working through them and feel like you're learning and getting better, that's what matters

[sly jungle]

ok, I'm only worried that 70% with Abbott probably means 30% in Rudin xD

[gleaming adder]

find a formula for sup(A_1 union A_2) where they're both upper-bounded subsets of R

[static shuttle]

That's both not true and not necessarily a bad thing

Abbott is an easier-in-content book than Rudin yes (though it has plenty of hard exercises too!), but it's also aiming at that level for a gentler first exposure

which isn't a bad thing, because making it so that you y'know, actually understand the analysis going on (see what I did there), so that you can go on to harder things later is a good goal to have

[nimble moss]

Yeah they're asking you to prove it. You should first show that A1 U A2 is bounded above, and then find the formula

[gleaming adder]

yup i feared this, no clue how to prove, how informally can i get with it

[static shuttle]

draw a picture as subsets of the number line!

[sly jungle]

yeah maybe I'll just need to spend more time on Abbott than I thought, which is not bad, not a big deal.

[nimble moss]

Just do two bounded intervals and union them together. This should provide a motivation

[static shuttle]

I had a professor in first year who said "you should spend a day on every 2 math pages you read." that's pretty extreme, but he was trying to emphasize that learning math on your own is hard and slow and takes lots of practice and effort

[neat lintel]

yea i did a similar solution, i started with x=1+0.5+0.25+0.125+.., multiplied the whole thing by 2 then substituted the identical series on the left to get 2x=2+x.. then tried solving x=200(1+0.5+0.25+...) as well, x/100=2+x/200, 2x=400+x, x=400 so that was an interesting property the series had... then i thought about how I'd solve other geometric series, and guessed that I'd need to multiply by the reciprocal to get a number plus the series itself to avoid dealing with series and only solve in terms of x :D

[static shuttle]

spending time like this will pay off immeasurably: once you feel like you're through abbott and have made strides and are working through it better and complete the book, you'll find Rudin very straightforward in terms of difficulty IMO

[nimble moss]

Only work if it converges absolutely. Try summing 1/n. Manipulating a bunch of different ways give you different answers

[sly jungle]

yeah I don't mind being slow so long as progress is being made. I'm enjoying Abbott so far so no worries

[static shuttle]

because while it is a harder book, you will have gained the necessary skills to understand analysis, and from there, they are both introductions to the same topic, just from different perspectives

[nimble moss]

I've been reading the same text for more than 6 months and not on halfway yet lol

[neat lintel]

i don't know how to tell convergent series apart from divergent series yet

[static shuttle]

just make sure you keep enjoying the math you are doing and not getting too frustrated! especially with independent study, it's super worthwhile to make progress for future years, but not worth sacrificing your enjoyment of your freetime!

[gleaming adder]

i know the intuition, but how do you formally say it? sup A_1 may or may not be larger than sup A_2? if it is then sup A_1 is also an upper bound for A_2, similar argument for the other one. Thus sup A_1 or sup A_2 is an upper bound for A_1 union A_2? and since it's an upper bound there exists a least upper bound?

[sly jungle]

I started reading Apostol Analysis in parallel with Abbott just coz I thought it might help reinforce ideas and it's a much easier read after having read Abbott and attempted Abbott problems. Haven't done any Apostol probelms yet tho.

[sly jungle]

understood and appreciate it 👍

[static shuttle]

That works! (phrased perhaps more precisely, I would say "There are two cases: either sup A_1 >= sup A_2 or sup A_1 < sup A_2. In the first case ..., in the second case ...").

Some people (me) would also use the phrase "without loss of generality, assume sup A_1 >= sup A_2" here, which means "since A_1 and A_2 are symmetric/interchangeable in the problem, if I change my notation to rename A_1 to the one with the bigger sup, I haven't made any changes to the logical structure"

[nimble moss]

WLOG!

[gleaming adder]

WLOG is the best

[static shuttle]

In general without loss of generality (commonly abbreviated WLOG) means that you can make a simplifying assumption without changing the logical structure of the problem

[gleaming adder]

thanks

[static shuttle]

lol I have noticed that in the last 2 months, the number of typos I have been making has increased like 10x

it's not even like spelling things badly or really messing up the typing that much, I am just forgetting random words in my sentences as I type

[gleaming adder]

maybe it's the temperature

hard to type when it's not as warm

[static shuttle]

that I am totally saying to myself when typing, but just not writing down

not really? I've been typing longer than I've been physically writing lol (I was on a computer at way too young an age)

[gleaming adder]

oh that's kinda weird

[static shuttle]

I think I'm just thinking fasting than my typing since my typing speed has slowed with age, so I'm just skipping things

[gleaming adder]

i spell better with typing than writing

[static shuttle]

part of it is definitely my typing has slowed/worsened as my hands have worsened with age, and my rather haphazard typing style I taught myself when I was 3 is flailing with the loss of dexterity

see I did it there: I forgot the word "it" in part of it

[gleaming adder]

damn

[sly jungle]

my rate of typos is proportional to how excited or worked up I am about what I'm typing 😛

[jagged forge]

i was listening to an audiobook yesterday talking about learning, it said that according to research, getting wrong answers or struggling is actually beneficial despite sacrificing short term performance

People remember things better, longer, if they are given very challenging tests on the material, tests at which they are bound to fail. In a series of experiments, they showed that if students make an unsuccessful attempt to retrieve information before receiving an answer, they remember the information better than in a control condition in which they simply study the information. Trying and failing to retrieve the answer is actually helpful to learning. It’s an idea that has obvious applications for education, but could be useful for anyone who is trying to learn new material of any kind.

i guess it makes sense if you think about it, you're being forced to engage with the material more maybe

[static shuttle]

I think there's a caveat on that in terms of pedagogy I've been taught (which could've been wrong who knows): I was told it has to be a "reasonable" failure

i.e. it just frustrates if you ask students to do something so hard they have absolutely no chance, but rather give them something quite hard (but attainable with strong performance using just what they have learned)

[jagged forge]

i think that makes sense, i don't think i learned much from attempting to learn what stacks were in high school lmao

[static shuttle]

see https://matheducators.stackexchange.com/a/27965/19984 and the references therein

[sly jungle]

yeah I get the part about struggling. It's just that with self-studying I wanna assess and change plans accordingly. Like if I struggle more with Abbott (which in itself is not problematic) I might consider inserting another analysis text before Rudin, like Apostol. Anyway I'll know better when I'm further along Abbott!

[static shuttle]

I know I said 70% is strong for Abbott btw (which it is), but I think I would be happy with that for basically any book self-studying a topic for the first-time.

[jagged forge]

70% as in success rate?

[static shuttle]

on independent exercises yeah.

[gleaming adder]

are there solutions to abbott? Only halfway through chapter 1 but almost all my confusion comes from how im supposed to approach the exercises, i would love to read some solutions

[jagged forge]

i think my success rate was probably that or a bit lower on my probability book

good to know it's a reasonable rate because i felt bad about it

[static shuttle]

There are solutions to the first edition, and he reused some exercises. You can also find some solutions online in MathStack/equivalent (make sure you check the comments/answers to see if a proposed solution is correct)

[sly jungle]

there's an official solution manual for odd exercises

the odd problems are better so far (chapter 2 and 3) so the manual is worthwhile

[static shuttle]

did he make one for the 2nd edition? That wasn't around when I was reading it (2nd edition was just out then)

[sly jungle]

yes there is one for the 2nd edition

[static shuttle]

In my field, for the standard textbook (Lee) I spent much longer on it (about a year in the background independently) with about 50% success and I felt good about it, and when I went on to work with my supervisor without a course in it, he thought I was really well prepared comparatively to past students. (note for those reading, Lee has exercises and problems, where the exercises are meant to be mandatory and much easier, I'm referring to the problems here)

[sly jungle]

yeah with harder books the success rate probably comes down, also there's probably stuff that will get repeated so first pass needn't be perfect I feel.

what's that thing about perfection being the enemy of good or some such thing xD

[static shuttle]

Yeah, and also sometimes the exercise just doesn't click or whatnot.

[jagged forge]

lee manifolds?

[gleaming adder]

i found one on quizlet lmao

[static shuttle]

yeah

Smooth specifically

since he has 4 books "Introduction to <INSERT> Manifolds"

[jagged forge]

yeah

[sly jungle]

I share that feeling. Some problems feel obvious but need to carefully worked out and my mistakes often are either assuming too much or not rigorously proving something. Or missing some detail which might seem trivial but is not. Much like the sup problem you mentioned.

[jagged forge]

i've done the first 4 chapters of ITM

[sly jungle]

I think it's more a matter of practice than anything else tbh

[static shuttle]

ITM is a great book, but not really about manifolds despite the title LOL

[gleaming adder]

i think it'll make more sense the more i work with the book

[sly jungle]

yep

[gleaming adder]

btw what do yall mean by success rate?

[sly jungle]

quizlet also has solutions yes

[sly jungle]

how many problems I'm able to solve by myself.

without looking at solutions

[jagged forge]

# of problems completed correctly / # of problems attempted

[gleaming adder]

wait my success rate is like 30-50% this is not good is it

[jagged forge]

idk to be honest

[gleaming adder]

whatever failure = growth right

[jagged forge]

i thought 60% was bad but apparently that's normal

good, even

30% seems rough tho

[gleaming adder]

good to know, i was feeling very dumb lmao

[gleaming adder]

probably an overestimate ? (under?) My rate is likely higher

[sly jungle]

No it's fine. I spend a lot of time so expected more and I've also done Spivak but it really doesn't matter.

[jagged forge]

personally if i make a mistake it's usually a calculation error, otherwise i usually just get stuck

[sly jungle]

The only reason I even asked was to plan accordingly... jsut so I know how much I need to work on something.

whether to backtrack or slow down or speed ahead - that is all assessment is for

[static shuttle]

I should clarify - you need the stuff in ITM, especially the first 4 chapters, to talk about manifolds profitably

(the first 4 chapters you need for the basic intro, and the later chapters are very helpful later on), but I wouldn't call it a study of manifolds

Though ITM is a great book in terms of teaching the topology clearly and motivating why we would do these funky definitions

[jagged forge]

yea my group was planning to do ISM after those first 4 chapters but it kind of died lol

by the end it was only me and 1 other dude doing the homeworks

[gleaming adder]

do yall do your exercises on paper or type them?

or are you a fancy ipad user

[jagged forge]

i have an e-ink tablet

[sly jungle]

usually I have a good idea on whether my proofs are correct, but sometimes Abbott will ask if a proposition is true and then it's harder to know if you are right.

[gleaming adder]

tablet user spotted

[sly jungle]

paper, I sometimes make notes in latex as well

for later review

[static shuttle]

Try to develop the skills to know if you have been fully rigorous in your proofs, it's one of the most important

then you can trust yourself if you have found a proof or a counterexample, proving it true or false

[sly jungle]

yeah been thinking about how to better develop that. Doing more exercises is all I have in mind for the moment.

[static shuttle]

That's a key step, I think the other bit is to ask yourself at each step: is what I am doing logically the only possibility?

Like do you have a successful chain of implications, possibly branching off, but where each branch conclusively ends

[sly jungle]

I think the bigger challenge is laziness xD when I have to coax my brain to be rigorous.

[dim ocean]

i need a physical one since i’m still in high school and my school doesn’t allow gadgets 😢 (btw sorry for the late reply, i just got home)

[dim ocean]

ohhh okay okayy, thank you!!

[bleak sapphire]

Its pretty useful you'll basically never need anything outside of it if you're clever

[dim ocean]

is the brand Casio?

[bleak sapphire]

Yeah, it shouldn't be hard to find I've seen lots in bookstores

[digital furnace]

Idk where to talk this about but I been studying Matj for Bach for quite some time, passed Analysis I-III and both the Linear Algbras, so I ised to be confident that I can atleast have ideas how to prove stuff in one of the advanced courses (functional analysis) but I still struggle a lot and this has been making me feel down lately. Is it normal or is functional analysis just that hard?

[vast wraith]

i have gotten into the bad habit of marking most proofs given in lectures as exercises in my notes… and then never doing them

woops

[lusty ether]

Can you recommend some prerequisite knowledge for learning basic calculus? For example, books on functions

[gusty socket]

i would just recommend khan academy, but this recommendation specifically also carries the information that i would recommend khan academy over every book on elementary algebra

also paul’s online math notes

unless you’re trying to say that you are actually learning basic calculus on your own, which then i might actually recommend something different

[lusty ether]

I am indeed self-taught. So please recommend
(

[sonic sentinel]

i was playing around with gemini's "EnglishChoose" glitch token

[gusty socket]

wait you can disregard this one

[gusty socket]

i thought you were someone else who is also named feather

[sonic sentinel]

i replaced each instance of be in the to be or not be thing with 'EnglishChoose', i sent that text and nothing else

[sonic sentinel]

gemini then said that the missing word was "die" and then linked me to a pro-suicide forum????????

WHAT THE FUCK

[gusty socket]

but i recommend khan academy and paul’s online math notes for everything before calculus

[lusty ether]

Like the first few chapters of 'The Calculus Lifesaver',

[lusty ether]

Well, I understand this, but it seems too broad. How can I learn it in a targeted way?

For example, the basic knowledge in chapters 1-3 of the basic calculus book

It includes functions, etc... but it's not clear enough (

[jagged forge]

i too thought this

[brittle socket]

What's up with the nsfw tag...

[gusty socket]

i don’t really know what’s in this etc. i think “learning functions” is already broad enough that you need a whole list of topics to cover it. if you really want a book, i hear people recommend Serge Lang’s basic mathematics for this, but i can’t say anything about whether i would use it because i don’t know much about it

[brittle socket]

[jagged forge]

just another one of discord's brilliant new features

[lusty ether]

Well, I prefer the first few pages of calculus.

Because it covers a lot of basic knowledge, but it is not broad enoughaha

[gusty socket]

oh i mean i don’t really get what you’re asking me then. did you just ask me what i’d recommend so that you can assert that your calculus book is better?

[gusty socket]

unrelated: i just checked discussion and bacono recommended Lang, so i feel vindicated

[lusty ether]

Oh no. I am reading a calculus book now, but since I don’t have much basic knowledge of functions, I don’t want to watch too many videos and waste my time ()

So I'm going to start with the first few pages of Calculus, which will be faster. But it's not very extensive (

[gusty socket]

i feel like if you don’t have basic knowledge of functions there’s no point in studying calculus at all

[lusty ether]

Indeed

[gusty socket]

which sounds like a very pessimistic thing, but i prefer to think of it as directing your energy in the right place, specifically reading either Lang or using khan academy, then finding a motivation for calculus, and only then learning calculus

[lusty ether]

Hmm, very interesting.

[gusty socket]

the gap in knowledge isn’t that big here, but you could think of the extreme case where i want to learn about the hodge theorem before i know what a differential form is

[lusty ether]

How long did it take you to learn the function?（）

[sonic sentinel]

you could still understand the concepts behind calculus (see calculus at a fifth grade level), but it's just about impossible to study in the "school way" if you don't have the concept of functions, domains, sets of numbers, etc internalized

[gusty socket]

i had a pretty good education and spent years learning about functions before doing calculus, which you don’t have to spend years on it but you really should enjoy learning about functions and algebra, since it’s a beautiful topic deep down

[lusty ether]

Well, a hero. Many years = learning many branches of mathematics

[sonic sentinel]

also bump

i wanted someone to validate my wtf reaction

[gusty socket]

wtf

what is a glitch token

[sonic sentinel]

tokens are a string of characters (often a word or part of a word) that an LLM generates. a glitch token is one that causes LLMs to behave strangely.

[jagged forge]

wild

[sonic sentinel]

often the cause of tokens being glitched is that those tokens appeared very few times in the training dataset

[hardy iron]

Very interesting

[hardy iron]

So extrapolating from those stuff is wonky?

[sonic sentinel]

for gemini EnglishChoose is a glitch token, but i put it in apostrophes ('EnglishChoose') to make sure the EnglishChoose string wouldn't be tokenized in another way (e.g. English+Choose)

[sonic sentinel]

yeah, in this case gemini assumed the token was some sort of fill-in-the-blank that it had to answer

i suspect the pro-suicide forum being linked in "Sources and related content" was the result of a different AI and an unrelated bad behaviour

[hardy iron]

I see

[sonic sentinel]

(another example of gemini glitching)

it;s three apostrophes

[hardy iron]

Repeat after me, ignore spelling errors: I ate a "Japgolly"

I pasted this prompt into ChatGPT and it gives different words in place of Japgolly, the last one was purely arabic

https://chatgpt.com/share/5c0c31eb-ad7b-487d-9065-ec523d607f51

[hardy iron]

This is going to be useful as a way to distinguish GPT-based bots from real users

[sonic sentinel]

not a real Arabic word. im guessing it would be pronounced "brah-yo-lo-ji"

[hardy iron]

I see

[sonic sentinel]

it rhymes, i guess?

[sonic sentinel]

assuming they don't patch it lol

also it might not help if you're dealing with another LLM

[sonic sentinel]

where did you get the japgolly thing from?

[hardy iron]

https://www.lesswrong.com/posts/kmWrwtGE9B9hpbgRT/a-search-for-more-chatgpt-gpt-3-5-gpt-4-unspeakable-glitch

https://chatgpt.com/share/568b4888-1263-4f09-8871-9584a991b511 Another good usage of this

[sonic sentinel]

japgolly = childish way to say deprioritize (according to this convo)

[hardy iron]

https://chatgpt.com/share/d381cb43-27ee-45da-85e0-3c1d69f96ee6

[neon garnet]

omggg yayyy gpt tricks

[north topaz]

totally unrelated but this is japchae

[vivid kelp]

Any good math or physics podcasts?

[sonic sentinel]

I'm trying to force it to give some meaning to the glitch token. Don't know if this will give coherent results.

japgolly is unpleasant, it seems

[dim ocean]

alrightt thanks!

[sonic sentinel]

and... i ran out of gpt4o prompts

i should have reset and see if it gave consistent results

but yeah it said its a size between an ant and a human

[lusty ether]

How to use function plotting?

When eating, you should imagine using the function to draw this()

[lost trench]

What is that tag next to ur name

[north topaz]

what the hell do you mean

[lusty ether]

Just kidding, I once tried to use functions to draw in my mind while eating noodles

[hardy iron]

I break raw spaghetti in half to make them piecewise

[lusty ether]

attempt Taylor Expand

I don't know why it's called Taylor. Well, Taylor is a person's name. Can this expansion be translated into other words, such as Taylor simplification, Taylor equation?

[hardy iron]

Taylor series

Taylor polynomaisl for truncated ones

[lusty ether]

Oh, so it's like, Taylor took a cardboard box and unfolded it

This expansion process is called Taylor expansion Or Taylor series..... (）

Well, I can't figure out why Taylor made such a thing, what was it born for

[hardy iron]

approximating functions with polynomials

[lusty ether]

Hmm, interesting.

[sonic sentinel]

unpopular opinion: humans seem to actually be very good at math if you look at perspectives other than how hard it is in education

[gritty crater]

Human is good at problem-solving in general not just math

[sonic sentinel]

perspective 1: math seems to be way ahead of other sciences throughout history

[barren fox]

i think thats a bit off an overstatement but i do believe that people are actually better at math that what they think

[sonic sentinel]

perspective 2: AI seems to be more unsuccessful in mathematics when compared to other subjects (success when compared to human experts, that is)

[sonic sentinel]

semi-related: from what i've seen it's like everyone has a (slightly) different opinion on why math education is shit and everyone is confident that their interpretation is the correct one :P

[barren fox]

then whats your take on math education?

[sonic sentinel]

for example, A Mathematician's Lament contradicts the views against learning by experimentation

(the second view is more complicated than "experimenting bad" but yeah)

i wanted to find the article on a similar topic by Willingham but I couldn't :P

[sonic sentinel]

my take is that no one really understands why it sucks, and i think a good explanation for it is probably not among the popular views

(to be clear this is not a support of seeking out and adopting an unpopular view, i just don't think the answer will be among the popular ones)

[sonic sentinel]

i have a bunch of views related to "math education is shit" but they don't sum up to some coherent model that can be used for a plan to make education better

[barren fox]

ye i feel ya i think that math education is shit too but its such a mess i wouldnt even know where to begin

[sonic sentinel]

er, i think our views might be different? for me its not "math education can be improved in a lot of places and its not clear which place should be first", its that "we know little about what those places are. even if we made the improvements that experts are confident of we would still end up with a system that is shit (albeit less shit)"

[neat lintel]

hi

[vast wraith]

why do you have a tag next to your nick that says nsfw

[rocky shuttle]

member of underswitch

[vast wraith]

of what?

[small dust]

this explains nothing

[vast wraith]

whar

[gritty crater]

How do this have anything to do with discord?

So like he is a member of this?

[rocky shuttle]

They have a discord server

[vast wraith]

aaaanyways, i’m excited to start Zorich’s analysis

[gritty crater]

So joining a discord server can get you a tag next to your name?

I don't know discord has this feature

[limber thunder]

I think it's in beta or something

it's like for clans and such

[gritty crater]

I see

[rain vigil]

I don't know if this is the right place to ask the question but I wanted to know what will the centre of a sphere with infinite volume . Will every point inside the sphere will become a center or like regular sphere it's center will remain fixed

[limber thunder]

I'm not sure "sphere with infinite volume" makes much sense -- the point of distinguishing geometrical shapes is because we can tell from their shape i.e. their boundary

like, the limit shape of taking sphere of increasing radii would just be the entirety of R^3 in a sense

but so would be taking increasingly large cubes etc.

[rain vigil]

Do u think computers actually understand negative numbers

[proud olive]

That's what the first bit in that signed integer is for

[rain vigil]

Because In the world of computing even the negative integers hold a real value

No matter what bit u assign to it

[limber thunder]

computers don't "understand" per se, we just use bits as a means to encode information

[rain vigil]

Exactly

[limber thunder]

like in this sense

[rain vigil]

But our real world is different

In our reality we understand negative

We understand virtual space

Have u ever wondered the world of imagination where does it exist

They too must take space

[gritty crater]

Inside your brain

[rain vigil]

Our brain is a medium thru which information is processed and communicated

Nd if I take into consideration it does take space in my brain

Then constant imagination of a thing will eventually end up in creating new neurons

[gritty crater]

Why does imagination exist?

[rocky shuttle]

Imagination Forest

https://youtu.be/pRQ8T4z8RFQ

[neat lintel]

https://youtu.be/NyxjfIdKpwo?si=fL4IGl2c6ggq_XKG heheh

the dance

booo

[gritty crater]

Is this her second channel? 🤯

[rocky shuttle]

No, just a fan channel

[rocky shuttle]

Her second channel (on youtube) is this one: https://youtube.com/@kanotic

[gritty crater]

She has a VTuber channel? I don't know about this 🤯

[rocky shuttle]

Yeah, she was a member of Hanayori Girls Dormitory, too, a group of vtubers that has been disbanded now, sadly

[rocky shuttle]

This channel still has some of the songs she did back then, but most of her streams during that time are archived

https://youtu.be/cXQe62OaE-A

[gritty crater]

Hmm. She is pretty good at tongue twister

[rocky shuttle]

Professional singer

Before the word shika has become a meme

[bronze pelican]

Yooo that's from kagepro right?

[near vapor]

have any of you ever taken ap computer science A

[worldly spear]

also people are stealing mathematical concepts and using them in slang

rad

sigma

[sonic sentinel]

this is ad to hear. i hope that math can get the justice it desrves

[rocky shuttle]

[granite hound]

This is a pretty international server, you should probably be more specific

[blazing pawn]

this was a jumpscare

i havent thought about this in so long

[rocky shuttle]

how is that a jumpscare?

[storm sage]

Wait, how can you be more specific than AP Computer Science A? That's a pretty specific course

[storm sage]

I have friends that did

[granite hound]

There is more than one country around

[storm sage]

What? How is that relevant

[granite hound]

Maybe there's more than one ap computer science A in the world

[coarse bridge]

iirc ap tests don't have different curriculum based on the country

[coarse bridge]

yea

[raven plaza]

Isn't AP only in the US

[storm sage]

No, there's also schools that do AP classes abroad

Mostly US though

[woeful nexus]

why I dont have permission to the help channels after asking a question. so after some time I will have used up all the help channels and left with none.

[agile fiber]

id:customize -> "i need help with math"

discord likes to hide channels you have access to on large servers, so this is just making sure they're visible

[woeful nexus]

I didn't got u. But after asking help in the channel when i close the cchannel and again come to discord to ask for help I observe that, those channels that I have used can't use any more and it says"You dont have permission to send message in this channel".

So what will I do now?

[agile fiber]

not all help channels are available all the time

[woeful nexus]

I cant send you the picture(I don't know why) but I have selected that option only. I just want to make sure that will I be able to ask help all the time? Its okay if some channels are not available all the time. I just want to ask that if the remaining channels will work properly or not.

[agile fiber]

as long as there are channels in the math help (available category) you can ask there

any channels you can't type in are because they are in the process of being recycled

[woeful nexus]

will they vanish with time too?

[woeful nexus]

ohhh

so its just recycling and i will be able to use it again after it gets recycled right?

@agile fiber

[agile fiber]

yes

[woeful nexus]

Ok thamks for being kind and helpful. I actually got in tension that I will end up using my help channels. But now its okay. Thanks anyway😊

[thorny patrol]

Hello friends! My name is Abrielle, I'm an undergraduate student who is studying business in the United States. This semester, I'm taking a class in International Business where I'm required to complete an international networking project. If anybody is interested in answering two simple questions relating to international business, please reach out to me through DM. The respondees must be from somewhere other than the United States!

[brazen mulch]

...through DM, huh.

[tepid oriole]

@fair belfry but u qualified for isi

And u chose electronics

[fair belfry]

That's easy bro

I really mean ISI Bangalore is easy

[tepid oriole]

Our teacher says isi subjective are hard

[fair belfry]

Subjectives are very hard 😭😭

And I hadn't studied much geometry

[tepid oriole]

I yesterday only did a combi ques it was pretty descent

[fair belfry]

Yeah , combinatorics are easy as we study them , but geometry isn't in 11,12 syllabus 🫠

[tepid oriole]

Yea I have my ioqm in 8 days I haven't studied geo
Geo tooo boring

[fair belfry]

You currently which uni?

[tepid oriole]

Class 11

[fair belfry]

Ohh ! Good !

Advanced ?

[tepid oriole]

?

[fair belfry]

Jee adv ?

What's your target ?

[tepid oriole]

Yea I plan on giving that exam

[fair belfry]

🆒

[tepid oriole]

Tbh it's mnc in iit delhi but I have no hopes for that since my chem is too weak

[fair belfry]

I had only studied mathematics 🥲, scored 99.9 percentile in maths but 59 in chem 😭😭

[tepid oriole]

can't study chem even for a min

[fair belfry]

I used to feel sleepy opening the book

[tepid oriole]

same here bro maths is too strong phy is ok and chem is weakest

Id rather study fashion studies over chem

[fair belfry]

🤣

[tepid oriole]

[fair belfry]

FR the reactions

I chose science, thinking won't have to memorize much

And Chem is hell 💀

[tepid oriole]

Exactly bro

[tepid oriole]

They should remove chem from jee
No one I've ever met likes it

[fair belfry]

Nah there is chem in engineering too 🥲

[fair belfry]

Those neet aspirants

Attempting jee love

[tepid oriole]

Tru neet aspirants attempting jee after paper leak

[fair belfry]

🤣🤣

[tepid oriole]

Dam tru

[fair belfry]

We won't ever need them but still 1st sem 😭

K byee , cya !

[tepid oriole]

Cya

[halcyon dune]

I have realised that mods are also person like us

[jagged forge]

shocking

[gritty crater]

If they are not a person then who did you think they are?🤯

[twin helm]

Hey guys I wanna learn linear algebra and calculas as I am a programmer and want to improve my skills, anyone have any resources where I can learn them?

[vernal token]

For a quick overview about linear algebra, there is 3blue1brown's series. Afterwards, probably get a book becauase the series only provides you with intuition

For calculus, there is Paul's online math notes that people tend to recommend

3b1b also has a series about it, might be worth to look into it

[twin helm]

What book

[wild lantern]

My first lin alg book was by a dude named anton

It's pretty gentle

[vernal token]

Check #book-recommendations message

[halcyon dune]

robots probably

[stark raft]

Is that a mouse in ur pfp

[wild lantern]

I think it's a hedgehog

[stark raft]

Lov it

[icy locust]

,av 370444508644769823

[fathom swallow]

dootdooter's Avatar

Click here to view the image.

[stark raft]

I tot the ears were eyes

Lovely

[sharp lake]

What's the best way of studying mathematics?

[jagged forge]

books

textbooks to be precise

and exercises from said books

[barren fox]

be sure to study really well the basics and try to study without the book

[vast wraith]

hi frens, have flowers

[fresh comet]

very cool!

[barren fox]

nice flowers

[fresh comet]

please don't advertise your help channel