help-39

[cursive wraith]

It's kinda pedantic to go and say that g is the identity map

since technically they are different sets

but they behave the same

because we can create functions like f and g

that link them perfectly

[worthy lance]

Pedantic is a pedantic word

[prime bramble]

hm, true

ah, welcome to mathcord!

for math help, see #❓how-to-get-help

is it a problem if I were to identify X x {p} with X, and then call g the identity?

[cursive wraith]

I don't mean to be pedantic about your pedantic remark, but "pedantic is a pedantic word" sounds like first order recursion

[prime bramble]

ig this is just identifying g with the identity?

is that really a problem?

[worthy lance]

I don’t mean to be pedantic, it is called redundant

[cursive wraith]

this seems very repetitive

[prime bramble]

what do you think, raf?

[warm current]

https://tenor.com/view/shallow-pedandic-pedantry-pedant-family-guy-gif-26075926

what does "identify" mean here?

[cursive wraith]

yeah but at the cornerstone, it's g that allows us to "identify" X x {p} with X

[worthy lance]

Sorry @prime bramble , our conversation had to be solved

[cursive wraith]

so calling it the identity seems far fetched

[prime bramble]

hmm

[worthy lance]

[cursive wraith]

like you're trying to show two things "A" and "B" behave the same

so you create a rule between them that maps perfectly the structure of one onto the other and vice versa

if you call that rule "the identity", then you're kinda losing the key point that A and B were only known to be the "same" because of that rule

[prime bramble]

that makes sense

[cursive wraith]

like saying f is the identity because A = B

and A = B because f exists

[prime bramble]

yeah, I see it now

darn

[warm current]

I need this

[cursive wraith]

that's my opinion, I don't feel qualified enough to go through the ped-on't you dare

[prime bramble]

then if I wanted to show that ${p|}_{X \times {y}}$ is a homeo between $X \times {y}$ and $X$, I'd need to go the long way?

[jolly parrot]

higher!

[prime bramble]

like, how would you justify this without writing a small paragraph?

p is the projection here

[prime bramble]

continuity and surjectivity are things I already know, but injectivity and cont of inverse would need a couple sentences

and I wanted to bypass all that by identification and then calling this map the identity, a homeo

[cursive wraith]

injectivity should be okay

[prime bramble]

mhm, one sentence

[cursive wraith]

suppose p(x1,a) = p(x2,b)

with (x1,a) and (x2,b) in X x {y}

then a = b = y since a,b in {y}

[prime bramble]

mhm

[cursive wraith]

and x1 = x2

bc p(x1,a) = p(x2,b)

so (x1,a) = (x2,b)

[prime bramble]

wait, what?

[cursive wraith]

p(x1,a) = x1

[prime bramble]

p(x1, a) = x1

[cursive wraith]

that's the def

[prime bramble]

yeah

[cursive wraith]

and p(x2,b) = x2

[cursive wraith]

hypothesis

[cursive wraith]

conclusion

[prime bramble]

oh no, I misinterpreted what you said

my bad

reading comprehension issues

[cursive wraith]

alr no problem

I'm guessing you're working with p : X x Y -> X

[prime bramble]

indeed

[cursive wraith]

so if you want to check that for an open set W of X x {y} with the subspace topology

p(W) is open in X

by the subspace topology, W = (U x V) n (X x {y}) for some U open in X, V open in Y

so two choices

if V contains y

p(W) = ...

if V doesn't contain y

p(W) = ...

[prime bramble]

wait...

[cursive wraith]

I just realized U x V is just a basis of open sets for product topology

[prime bramble]

aren't we working with the restriction of p?

[prime bramble]

and this yeah

[cursive wraith]

p(W) = p_|(X x {y}) (W)

since W is a subset of X x {y}

[prime bramble]

ah, okay

[cursive wraith]

and the fact that U x V is a basis is ok

just work with basis of open sets

if it's true for a basis of open sets

by properties of image of union

it's gonna work for all open sets

[prime bramble]

yeah okay, but I really wanted to avoid going through all this haha

when is it okay to just call smth obvious

[cursive wraith]

if an exercise is asking you to do this

they don't want you to pull the obvious card

[prime bramble]

they are asking me to prove that if Y is discrete, and p is a projection on X, than p is a covering map onto X

like, on the one hand, I don't like leaving any detail out of my proofs

but on the other hand, justifying absolutely everything is one of the problems that make my proofs end up taking 3 pages

and I've been criticized in the past for writing too much

but I can't let tiny things go either

[cursive wraith]

omg you're doing covering spaces

[prime bramble]

yeah

[cursive wraith]

welcome to geometry

[prime bramble]

I'm glad to be here

[worthy lance]

Dash

[prime bramble]

this is a huge problem for me tbr

snow has gotten frustrated with my writing in the past

[cursive wraith]

don't worry, corrections also take 3 pages

[prime bramble]

I want to understand how to just call smth obvious and move on

[cursive wraith]

especially in geometry

[prime bramble]

but idk when I'm allowed to

so I never do

[cursive wraith]

I know how hard you want to call smthg obvious, the problem in geometry is, at some point, you're gonna realize that obvious isn't anymore

[prime bramble]

technically I'm not doing geometry yet ig

there's no notion of a metric so far

[cursive wraith]

like I said the fundamental group of some shape was homeomorphic to Z/3Z

[prime bramble]

this is just very basic alg top

[cursive wraith]

but it was actually some very fed up thing

but I didn't push further

cause "duh obvious"

[cursive wraith]

poor soul

you think metrics are still relevant

[prime bramble]

I feel like there's a difference between calling a fnd grp homeo to smth, and needing to justify why some map is open

[prime bramble]

but they are, are they not?

geometry and topology are not one and the same

you do geometry, you need smth in order to get lengths and angles and areas

[cursive wraith]

uh

[prime bramble]

you do topology, you don't

[cursive wraith]

maybe you haven't been introduced to Geometric topology

[prime bramble]

my interests lie somewhere there

doesn't it also depend on what part of geometry you do though?

[cursive wraith]

but like to say topology is not everywhere at high level geometry is a really big delusion

[prime bramble]

I haven't seen any geometers say that before

don't ppl need metrics to talk about e.g. connections?

[cursive wraith]

connections?

you mean connected spaces?

[prime bramble]

https://en.wikipedia.org/wiki/Connection_(mathematics)

[cursive wraith]

no, you need continuous and onto maps to {0,1}

[prime bramble]

no, connections

the thing in geometry

[cursive wraith]

ok sorry connections

[prime bramble]

also stuff like curvature, no?

I was under the impression that geometers care about this stuff

is that not the case

[random ermine]

why r we talking about connections

[prime bramble]

idk

this went far off my initial question

but the question has been resolved, so to speak

[cursive wraith]

I'm not saying that you will always work with TOPOLOGY and nothing else but topology in geometry

[random ermine]

no u don't need a metric afaik but with a metric u get a canonical connection called the levi-civita connection

[cursive wraith]

but whenever you're working in geometry at high level

you have piles of topology building the structure under you

[midnight haven]

Hi

[prime bramble]

of course

[midnight haven]

Do you need help with anything

[prime bramble]

nobody is denying that the topological structure is important

[random ermine]

get out

[midnight haven]

How do you find people to help then

[cursive wraith]

and most of the times the topology is at the same level

[prime bramble]

welcome to mathcord! check out #❓how-to-get-help for math help

[midnight haven]

Actually I'm just going to leave and do nothing

[prime bramble]

wdym by that?

I'm still getting into both geometry and topology

so I'm kinda new to stuff

most of the people I talk to on this server about math do geometry kind of

hi cat bit

can you teach me geometry

[random ermine]

u can do geometry with or without calculus

[merry carbon]

(Not great at it )

[prime bramble]

what does without calculus look like?

[random ermine]

btw the christoffel symbols are the connection components of levi-civita

[random ermine]

i guess alg top

[prime bramble]

Christ awful symbols

[random ermine]

and alg geo

[prime bramble]

but is that geometry or is that topology

ig the distinction is unclear

[prime bramble]

oh fair

issue is that AG scares me

I lean more on the DG side

[warm current]

My book even makes a point to be super aware of this

[random ermine]

same thing ig?

[prime bramble]

@random ermine @merry carbon do either of you have advice on when it's okay to call something obvious or clear?

or SWR

[random ermine]

actually i think u use calculus in some places for alg geo

[prime bramble]

this issue has been haunting me forever

[random ermine]

depends on ur audience

[prime bramble]

oh well, then I'm screwed

I write my proofs as if I was going to read them

but when I read proofs, I hate missing any amount of detail whatsoever

so I spell everything out

and my proof ends up being 3 pages

and ppl get mad at me

[merry carbon]

Same me knowing myself, I know that if I don’t put in all details, there’s gonna be a moment where I refer back to what I have and wonder why the simplest step even holds for however long, until it clicks and I start reconsidering life

Don’t think I have a great answer for where the line is (esp as how quickly things come, at least to me, depends on the day)

[warm current]

pretty much what chart and christ already said. If you are thinking to yourself "it is obvious", then you better be damn sure it is. I've messed up some really important bits of proofs because I thought I understood it.

[warm current]

Truth. snow turned one of my ten page proofs into half a page

[prime bramble]

yeah but ppl like snow have been commenting on my massive word count for months now

[warm current]

I like wordage.

[prime bramble]

I wrote 2 pages, and he told me to delete half of it

and then cut down the rest by like 80%

it's stuff like this that makes me wonder how one knows where to cut things

[warm current]

brevity may be the soul of wit, but verbosity is the soul of logic

[cursive wraith]

You have to try and do mocks

[prime bramble]

my TAs don't!

do mocks?

[cursive wraith]

like mock exams

you take some exam

and you set yourself a level of "rigor"

[prime bramble]

[cursive wraith]

like up to what point do you think you don't need to justify more

[prime bramble]

I can never tell idk

[cursive wraith]

finish in the allotted time

[cursive wraith]

that's the point

do it multiple times

and the goal is to finish almost 100%, and to not have a lot of free time when you're done

[warm current]

are you self-studying or in an actual class?

[prime bramble]

both

and in both cases, I write too much

[cursive wraith]

if you didn't finish the mock exam or ran out of time, means you spent too much time on questions

so try to soften the rigor

[prime bramble]

but it could be the case that I just didn't know how to answer the questions

[cursive wraith]

forgetting about the questions you don't know how to answer

[warm current]

In your proofs, I've found your wordage satisfactory, but maybe we're both messed up like that

[cursive wraith]

if you feel like you could have completed many more questions in the alloted time but couldn't because you spent too much time on details

spend less time on details

if you completed as many questions as you could but you have too much time to spare at the end

spend more time on details

[prime bramble]

hmm

that's an interesting metric to go by

[cursive wraith]

that's how I self actualize

I know that sometimes stuff can just "be that easy"

[warm current]

that classic moment at the start of an exam where you realize you don't know a single thing

[prime bramble]

ic

[warm current]

Allow me to offer a counterpoint to raf

I write my homework like notes

I write it with the intent that I can go back to it years later and basically re-learn the problem from what I wrote

I write my exam solutions with a "the grader knows what I am talking about" mentality

It really depends on how much you plan to use your old homeworks as notes for the future

[cursive wraith]

yeah, at least homeworks are not on time constraints unlike exams

[warm current]

but it's def important at least know how to do be either thorough or concise

I've definitely run out of times on exams from my wordage

But I also type 24/7, so when having to hand-write, it is extremely uncomfortable

[prime bramble]

hmm

I will keep all this in mind

thank you for all your inputs everyone

thank you: SWR, raf, mayer, chartbit

okie dokie, I shall close this now

[warm current]

.coose

[prime bramble]

I enjoyed the conversation, and I hope you all have a wonderful day

.solved

[pearl pond]

Channel closed

Closed by @prime bramble

Use .reopen if this was a mistake.

[warm current]

every day with @prime bramble and @merry carbon is a wonderful day

[prime bramble]

https://tenor.com/view/hug-love-kanna-cute-kanna-kamui-gif-17266781

[unkempt yacht]

chartbit

more like

chartbased

[pearl pond]

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[golden jetty]

can anyone help me integrate this

[golden jetty]

first time integrating anything ever teacher just didnt teach us anything

from my understanding we find the antiderivative of x first then evaluate F(3) - F(0)?

[mystic bison]

thats exactky what you do

[golden jetty]

aight

isnt the antiderivative of x

[mystic bison]

whole thing is multiplied by a negative sign tho

so

[golden jetty]

like

1

[mystic bison]

keep that in mind

[mystic bison]

the derivitive of x is one

the antiderivitive isnt

[golden jetty]

oh

[mystic bison]

do you know what a anti derivitive is

[golden jetty]

isnt it like the original function before the derivative

kind of hard to explain

[mystic bison]

yes

thats right

[golden jetty]

okay

[mystic bison]

did u learn how to do it?

if not this ones really easy

so i could just tell u

[golden jetty]

can u tell me please

[mystic bison]

so for this one

we would use the power rule

in integration

[golden jetty]

wait dont

tell me

[mighty bolt]

you add one to the power and multiply it by the reciprocal of the power you get from adding one

[golden jetty]

is it

x squared over 2

[mighty bolt]

yessss

[mystic bison]

correct

[golden jetty]

and then do i evaluate F(3) - F(0)

?

[mighty bolt]

👏

yessss

[mystic bison]

negative x ^2 over 2

[golden jetty]

or yea

[mystic bison]

not positive

and yes

thats the final answer once u evaluate

[golden jetty]

okay thank you guys so much

!!

[mighty bolt]

since there is a neg you coudl do F(0) - F(3) instead

hope youre successful!

[golden jetty]

thank you!

so the answer would be the same for this one too

since the bounds are switched

?

[mighty bolt]

nooooo

thats after you destribute the neg

i mean ig its the same but idk

i wouldnt say you should do that

[golden jetty]

okay

[mystic bison]

its kinda redundant

just solve it correctly

its easier that way anyway

[grizzled dust]

$\int_a^b f(x),dx = -\int_b^af(x),dx$

[jolly parrot]

from math import sqrt

[mighty bolt]

its right, i just wouldnt do it so you dont get confused

yea

[golden jetty]

thanks!

[mighty bolt]

youre welcome 🙂

[golden jetty]

.close

[pearl pond]

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[pearl pond]

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[flint wyvern]

am i right with A here? this is what i did but am i correct

[mint wave]

you already have another channel with this same problem...

[flint wyvern]

i dont

well i closed it

i just want someone to confirm

.close

[pearl pond]

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[pearl pond]

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[flint wyvern]

am i right with B here?

[brisk steeple]

4/5 (1/4)^(n-1)

Yes

[flint wyvern]

thank you are you sure it wouldnt be D

im confident with B though

[brisk steeple]

Put n = 2, then a_n = 4/5(1/4)^2 = 1/20, which gives the third term not the second one.

[flint wyvern]

wait so C??

i think i get it

[brisk steeple]

Uhm, why C now?

It's B

The common ratio is not 4/5, you can remove A and C from here.

[flint wyvern]

oh man im so dumb i understand

sorry its 1am 😭

[brisk steeple]

No problem

!done

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

[flint wyvern]

.close

[pearl pond]

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[pearl pond]

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[brisk steeple]

Q. Why is the graph of x^3 + y^3 + 3xy = 1 a line?

[inland ivy]

do you know the factorisation of x^3+y^3+z^3-3xyz?

[inland ivy]

it's not just a line by the way

it's a point and a line

[brisk steeple]

(x+y-1)(x^2 + y^2 + 1 - xy + y + x) = 0
x+y = 1
Or x^2 + y^2 = xy - x - y - 1

[inland ivy]

Not quite

Oh no wait it's correct

My bad

[inland ivy]

So yhe first factor gives you a line

[brisk steeple]

what about x^2 + y^2 = xy - x - y - 1

[inland ivy]

See what you can do with the second one

[brisk steeple]

ok

[inland ivy]

Try completing some squares

[brisk steeple]

what do i do with xy?

[inland ivy]

think of (x-y)^2

[brisk steeple]

(x-y)^2 + (x+1)(y+1) = 0

[inland ivy]

well that is indeed right but that's not what we're looking for

we want (...)^2+(...)^2+(...)^2=0

[brisk steeple]

can we express y in terms of x and find values for which there is a real pair (x,y)?

like this

I guess so

there is root(-(x+1)^2) = i(x+1)
So for a real value of y, x + 1 =0 or x = -1 and y = -1

thanks

.close

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[pearl pond]

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[muted notch]

Howdy

[brisk steeple]

hi, but what's the question

[mighty bolt]

Lmao

[muted notch]

What kind of question

[mighty bolt]

What is the math problem you need help with

[brisk steeple]

if you want to talk, you can go #discussion

[pearl pond]

@muted notch Has your question been resolved?

[pearl pond]

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[knotty geyser]

Can someone pls explain how to do this question? It's from AP Calculus AB. (also why is there a help forum page and then help channels which one am i supposed to post my questions in)

[mighty bolt]

You jsut take the derivative again

You got it

It’s the same notation for a second derivative it just looks a little weird

[knotty geyser]

the second derivative is cos y? which is different from the answer...

[mighty bolt]

Yea think so

But since you’re taking the derivative in respect to x not why when you take the dervativs of why you have to include dy/dx

Its cos y times the first derivative

Which is why the answer is what it is

It’s the same as implicit when you take the derivative of y you always have to put dy/dx after

Do you understand?

[knotty geyser]

no...im trying to find similar problems online

[mighty bolt]

I can give you an example

Those might be too complicated

[limber glacier]

If u had y = sinz, and z was a function of x, what is dy/dx

[mighty bolt]

They are in calc 1 not 3 pls don’t confuse them

[limber glacier]

Ok OK I don't know what the different numbers really mean

Calc1 vs 2 vs 3

[mighty bolt]

Yes

[mighty bolt]

I’m not trying to be rude i just don’t want this to be harder than this has to be I’ve already tried to explain it once and they didn’t understand

[knotty geyser]

waitt i think i've found a solution

[mighty bolt]

Yesss

Good job

[knotty geyser]

ohh ok thanks guys

.close

[pearl pond]

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[mighty bolt]

You’re welcome ❤️

[pearl pond]

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[worn lotus]

hey how can I prove this?

[cursive wraith]

induction?

[worn lotus]

yes induction but I don't know how to prove this with induction

[foggy mason]

n²+2n+1

[sharp smelt]

$a_1=2(0)+1$

[jolly parrot]

A dense set(Ping when reply)

[sharp smelt]

Try starting off with a_1

[worn lotus]

So that should be the base case right?

$a_1=2(0)+1$

[jolly parrot]

JC

[sharp smelt]

I think so

[foggy mason]

a_1 = 2(0) + 1 = 1²

its better

[worn lotus]

What should my next step be

prove for n+1 right

[foggy mason]

yes

[worn lotus]

and you can do that with replacing n+1 with n?

[foggy mason]

no

you need to prove that a_n+1 = (n+1)²

by supposing that a_n = n² is true

so, use the expression of a_n+1

[worn lotus]

And how can I do that?

[foggy mason]

use a_n+1 = a_n + 2n +1

its pretty straight forwarded

[worn lotus]

I found this really difficult sorry

[foggy mason]

just switch a_n with its values and its done

[worn lotus]

Wait let me think

[worn lotus]

can you maybe draw the steps

[foggy mason]

Suppose the proposition : "a_n = n²" is true
let prove that "a_{n+1} = (n+1)²" is true
we have a_{n+1} = a_n + 2n + 1
a_{n+1} = n² + 2n +1 = (n+1)²

[worn lotus]

I don't understand this part. So the first rule comes from the exercise right. How did you come up with the last?

[foggy mason]

(a+b)² = a²+2ab+b²

[worn lotus]

oooh

do you also need to prove the base case?

[foggy mason]

no, its a proof by induction

[worn lotus]

thanks

.close

[pearl pond]

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[midnight haven]

yes

because elemental functions are continous

still continous

limits

[pearl pond]

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[faint shore]

This shit gives me .70 in my calc, how do I find the actual ratio root 2/2

[faint shore]

Not something I can do with my calculator hey?

I'd have to have a reference of the unit circle yeah?

[versed mica]

lol

[faint shore]

Wut

How did u get that

[versed mica]

magic

[faint shore]

Might just be frl

[versed mica]

just use triangles

45-45-90

[foggy mason]

my calculator does magic

joke aside, its a scientific calculator so huh it sometimes gives some values in fractions

[faint shore]

I have a ti 83

plus

[pastel lagoon]

casio > ti

[versed mica]

you’re wrong

[faint shore]

Should I cop one

[versed mica]

ti-84 >>

[versed mica]

get the ti-84 plus CE

[faint shore]

Seen Math Sorceror say ti83 solos

[versed mica]

math sorcerer is like 50

[faint shore]

LMAOOO

[spring patio]

does it give you a fractional value for any input? try a random angle and see if it expresses the answer with square roots and such

i feel like it shouldn't

[foggy mason]

for all the angle in the unit circle it does

[faint shore]

Yooo I figured it out I think

[foggy mason]

pi/12 too

[spring patio]

pi/6, pi/4, pi/3, & pi/2 ?

[foggy mason]

yes

[spring patio]

ah that's cool

[faint shore]

Nvm lol

[spring patio]

you could do that manually too

but some just take time and it's useful that some calculators have those stored

[faint shore]

Man this shit so ass bruh

[spring patio]

your calculator?

[faint shore]

Yes bro

[spring patio]

real

[faint shore]

With fractions it's so rough

You gotta be mad careful with it, putting everything in brackets ns hit

[spring patio]

i think that's the struggle of every calc user

does it come with a d/c operator? your calc

[faint shore]

Idk what that is

[spring patio]

it's what converts a rational decimal to a fraction

like 0.33... to 1/3

[foggy mason]

a b/c <=> d/c

[spring patio]

sorry .33

[frosty sedge]

Sometimes you can square and then square root answer and it gives as a surd

[faint shore]

I tried it but it doesn't work

[spring patio]

yeah only for rational numbers

it can't figure out a fraction for sqrt(2) since it's irrational

[faint shore]

Lame asf

[faint shore]

Yeah dat's wat I figured

[frosty sedge]

Try to square and square root

[faint shore]

I woulda been surprised if it did figure it out, that woulda been sum crazy programming

[spring patio]

agreed, unless it was just stored

[faint shore]

Gnarly😭

[foggy mason]

lmao

[faint shore]

This is the goat calculator tho yeah?

[foggy mason]

texas instruments
never bought one

[faint shore]

What say u

[foggy mason]

i've never bought one i mean

[faint shore]

What are you rocking w/

Sum1 said Casio better so it's tripping me out rn

[foggy mason]

.

[faint shore]

Oh that was u hu

huh

Word

Okay thanks guys

.solved

[pearl pond]

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[faint shore]

What is this telling me exactly? I understand that if (- x - x -) = -, and (- x -) = +

[faint tundra]

when f(x) = f(-x), the function is even
when -f(x) = f(-x), the function is odd
it can also be not odd and not even

[faint shore]

I understand this

Now why is this relevant to the trig functions, and why do we need to know this, how did they figure it out?

[faint tundra]

the trig functions are functions themselves, it is stating a fact

[faint shore]

So it's just saying "dis wat it be" yeah? Not building up on my previous knowledge, yeah?

[faint tundra]

I assume you can prove these properties with identities

[faint shore]

ty

[faint tundra]

with the unit circle

[faint shore]

.solved

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[idle parrot]

????????

[languid viper]

you're cooked

💀

[mild blaze]

1?

x=1?

[idle parrot]

how do i prove it

[mild blaze]

replace x by 1

[idle parrot]

zengus

[idle parrot]

how do i prove it

[muted notch]

Zengus…

[idle parrot]

guys

[mild blaze]

i will help you only if u help me

look at aerostatik channel

[pearl pond]

@idle parrot Has your question been resolved?

[pearl pond]

@idle parrot Has your question been resolved?

[pearl pond]

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[torn sky]

How can i proof that they're the same?

log(10^0.699) = 10^log(0.699)

[torn sky]

If we take the rule that 10^log(a) = a

[exotic scaffold]

use properties of logs

[west sapphire]

i assume this is log base 10, otherwise it's false

[torn sky]

How'd we go about this?

I understand that we can make lg(10^0.699) into 0.699*lg(10)

[plush bramble]

,tex .log rules

[jolly parrot]

riemann

[torn sky]

Just showing the rules doesn't make me understand it, I have the rules myself in my book

How could we else write 10^log(0.699)

[mental wigeon]

take log

you have this

10^log(0.699) = y

take log both sides

log(10^log(0.699))=log(y)

now apply log properties

log(0.699)log10 = log(y)

log(0.699) = log(y)

y = 0.699

So we conclude 10^log(0.699)=0.699

[plush bramble]

You should try something yourself first

[versed mica]

you’ll understand it by using the rules when doing problems

[pearl pond]

@torn sky Has your question been resolved?

[torn sky]

hm alright, so we just take log on both sides like, and by using the rules it should come out like so?

log(10^0.699) = 10^log(0.699)

log[log(10^0.699)] = log[10^log(0.699)]

log[0.699*log10] = log(0.699)×log(10)

log(0.699) = log(0.699)

0.699 = 0.699

[mental wigeon]

good

[torn sky]

thank you 😄

.close

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[pine rivet]

im unsure how they get those values for E when switching to polor coordinates

[sharp vigil]

0 < theta < 2pi covers the entire plane

[pine rivet]

what about r?

[sharp vigil]

we have x^2 + y^2 = r^2 (you can get this directly from the conversions)

[pine rivet]

does it change when you switch to polor coordinates, because they stay the same i think as prior to the change?

.close

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[carmine zinc]

been on this for quite a while now, i dont get how to solve it

I tried putting in the values of 5/6, 3/2 and i got c <= 1

but the graph doesnt make sense for c=-4, unless im misinterpreting it

[spiral pivot]

Differential calculus?

@carmine zinc

If so, have you taken the derivative yet?

[carmine zinc]

on differential equations

[spiral pivot]

Ok, so c = 4 is the solution I arrived at. Not -4. Perhaps you just have a sign error?

[carmine zinc]

i dont think so at least, but i do need to revise my calculus a bit

[carmine zinc]

what did you do?

[spiral pivot]

Take the derivative, set it to zero, solve for the min and max in terms of c.

[carmine zinc]

oh

oh yea

i forgot i could do that lol

thanks xD

[spiral pivot]

No worries, I'm curious how you got -4 then

[carmine zinc]

at first i was too lazy to take the derivative, so i used the minimum and maximum values of the function

put them in, and solved for x

that gave me a discriminant of (1-c)^0.5

[spiral pivot]

I'm not sure how you found the minimum and maximum values of the function without the derivative.

[carmine zinc]

i didnt

the minimum and maximum are given in the question

5/6, 3/2

[spiral pivot]

Ooooh ok

[carmine zinc]

and (4-c)^0.5

[spiral pivot]

But those depend on the point of evaluation

[carmine zinc]

wdym>

[spiral pivot]

You know that f(x, c) = 5/6 for some value of x and c, and at a particular value of c, the function is a minimum there

But you don't know where it is

[carmine zinc]

no, i assumed c was constant

parametric functions arent in my syllabus

[spiral pivot]

So c is either a constant or a variable dependent on how you view the problem.

You can treat c as a variable to get a larger perspective on the function, but it might not be useful

[carmine zinc]

nah, c is definitely a constant, even if i had been taught them, c's value is always fixed

[spiral pivot]

I don't think you understand my point.

But that's not important

The idea is you use the derivative to find the location of the max and min depending on the value of c

[carmine zinc]

where do you think i went wrong then? i still dont get what was actually wrong with my approach

[carmine zinc]

that i understand

[spiral pivot]

This is the problem ^

[carmine zinc]

i thought you were talking about what i did though

[carmine zinc]

i know you can take the derivative to find it

[spiral pivot]

Hold up for a second and let me explain the full process

Because finding c isn't the end

Or rather, finding the location of the max and min in terms of c isn't the end

Because that's all you're doing by taking the derivative

You'll get x = g(c) and x = h(c) where g and h are some sort of function of c.

And this represents the max and the min

[carmine zinc]

uh huh

[spiral pivot]

Then you find 5/6 = f(g(c)) and 3/2 = f(h(c))

This gives you a method of solving for c.

Explicitly

[carmine zinc]

yea i know how to solve it with derivatives

[spiral pivot]

Ok

On the other hand

Your other approach, as I understand it, was you had the maximum and minimum and use tried to use that to solve for c directly

However, this would be f(xmax, c) = 3/2 and f(xmin, c) = 5/6

This is 2 equations and 3 unknowns

You need some other piece of data

[carmine zinc]

what's wrong with using the quadratic formula?

[spiral pivot]

Because you don't know xmax or xmin

[spiral pivot]

What does using the quadratic formula get you here?

[carmine zinc]

lemme use latex for a sec

,tex $\frac {x^2+x+c}{x^2+2x+c} = 5/6

[jolly parrot]

Supernova
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[carmine zinc]

Then simplify then solve for x with the quadratic formula, which will give you a upper bound on c

[spiral pivot]

[ \frac{x_{min}^2+x_{min}+c}{x_{min}^2+2x_{min}+c} = 5/6 ]

[jolly parrot]

OmnipotentEntity

[carmine zinc]

yup

[spiral pivot]

So you have a bound on c

But

[carmine zinc]

the xmin part doesnt matter for my purpose though

[spiral pivot]

You don't have a value for c.

[carmine zinc]

i dont need it, I just need a bound good enough for the options

[spiral pivot]

And this bound only eliminates one option

-4

[carmine zinc]

hmm?

it should eliminate +5, no?

[spiral pivot]

5 > 1 no?

[carmine zinc]

oh

ah

sign error

oh

the other limit is better, it eliminates both -4, 3

[spiral pivot]

Coin flip is ok

[carmine zinc]

hmm, this is still quicker than taking the derivative, tho

[carmine zinc]

, xmax=1

[spiral pivot]

The denominator of the derivative doesn't matter

[carmine zinc]

what?

[spiral pivot]

For solving for the max and min

[carmine zinc]

the denominator doesnt matter>

[spiral pivot]

You have (f' g - g'f) / g^2 = 0

You multiply through by the g^2

[carmine zinc]

oh you mean that

[spiral pivot]

So it doesn't actually matter

Except for pointwise discontinuities

[carmine zinc]

yup

[spiral pivot]

So taking the derivative isn't actually slow in this case

You don't have to compute g^2

[carmine zinc]

yea i guess

.close

[pearl pond]

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[carmine zinc]

Thanks!

[pearl pond]

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[wet scroll]

Can someone explain to me how we would solve this integral

Same method used in the picture

[summer imp]

They are skipping a lot of steps but the idea is to use different substitutions for both, i.e. u = 3-x and v = 1-x, and then it's just a power rule for both integrals

They are doing it by thinking ahead at what could be a function whose derivative is sqrt(3-x), kind of like undoing the chain rule.
But that's essentially u-sub, informally

[wet scroll]

alright. thank you

.close

[pearl pond]

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[woeful harness]

is this correct so far?

ik i have to prove it going from right to left after

but i feel like the second line is missing something

[cursive wraith]

there is some x-hat in the intersection that isn't in one of the B_lambdas?

[woeful harness]

oh

[cursive wraith]

what's the link between x and xhat as well

[woeful harness]

it should just be theres some xhat st xhat is not in B_lambda ?

[cursive wraith]

but what's the link with x?

[woeful harness]

just to distinguish were talking about a specific x

[cursive wraith]

?

so the xhat has nothing to do with the x you "let"

?

[woeful harness]

it does

[cursive wraith]

well what is the link

are they different elements?

[woeful harness]

i let x be an element of the entire thing

which means x cant be in the intersection B_lambda , so there must be an x (xhat) that is not in one of the sets

heres the containment right to left

[cursive wraith]

but

the x is well known

if you start calling it x hat you make people think it's a different x

when it's exactly the x in "Let x in ..." that we keep working with

you're mixing it up with the INDEX

if x is in the union of (...)

indexed by $\lambda \in \Lambda$

[jolly parrot]

rafilou is not not born in 2003

[cursive wraith]

that means x is in one of those sets

indexed by SOME $\lambda$

[jolly parrot]

rafilou is not not born in 2003

[woeful harness]

so lambda should have the hat?

[cursive wraith]

give the index you consider any name

and indeed that would make more sense

as to not confuse with the OTHER lambda that index the union

[woeful harness]

so the second line would be there exists an x such that x is not in some B_lambdahat

[cursive wraith]

no

there exists a LAMBDAHAT

such that x is not in it

x already exists

you let it exist yourself

at the first line

but lambdahat was never introduced

[woeful harness]

i see

it makes sense

[pearl pond]

@woeful harness Has your question been resolved?

[pearl pond]

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[unborn bone]

I have
i. doesn't work
ii. not as good
iii. not as good
iv. BEST

[pearl pond]

@unborn bone Has your question been resolved?

[unborn bone]

<@&286206848099549185>

[pearl pond]

@unborn bone Has your question been resolved?

[unborn bone]

.close

[pearl pond]

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[light canyon]

Jamie graduated from flight school and decided to take her friends on her private jet for a ride. She flew over a desert and from the plane, they saw a sandpit further ahead. From the plane, which was 853 m above ground, they observed two opposite points on the sandpit. The angle of depression from one point is 32° and the angle of depression to the opposite point is 45°. How far is it across the pit to the nearest meter if Larissa knew that the angle between both lines of sight is 80°? Include a diagram. (Round final answer to the nearest tenth).

[light canyon]

I am a little confused with the concept here. I don't get the last part where it says the angle between both line of sight is 80 degrees.

[cinder orbit]

hey

i'm doing a math problem:

What is the smallest positive integer N such that the value 7 + 30N is not a prime number?

[next estuary]

lmaoooo

[cinder orbit]

<@&286206848099549185>

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[pearl pond]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

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[cinder orbit]

oh sry

didn't realize i was in a chanel

[next estuary]

6

[pearl pond]

@light canyon Has your question been resolved?

[light canyon]

Jamie graduated from flight school and decided to take her friends on her private jet for a ride. She flew over a desert and from the plane, they saw a sandpit further ahead. From the plane, which was 853 m above ground, they observed two opposite points on the sandpit. The angle of depression from one point is 32° and the angle of depression to the opposite point is 45°. How far is it across the pit to the nearest meter if Larissa knew that the angle between both lines of sight is 80°? Include a diagram. (Round final answer to the nearest tenth).

this is a 3d structure btw

[pearl pond]

@light canyon Has your question been resolved?

[light canyon]

<@&286206848099549185>

[pearl pond]

@light canyon Has your question been resolved?

[pearl pond]

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[pure rapids]

Connect px,xb

[pure rapids]

Do you know angle properties of cyclic quad?

[full barn]

yeah

[pure rapids]

Let PAX = XAB = angle x

Now what else is also angle x?

[full barn]

no idea

[pure rapids]

XPB and XBP

Then what can you say abt triangle XBP

[full barn]

equilateral?

[pure rapids]

No

Look at it

[full barn]

angle x = XPB and XBP right?

[pure rapids]

Yes

Isoceles

[full barn]

how tho if all 3 are equal

[pure rapids]

Not equi

[pure rapids]

Theyre not

PXB is clearly bigger

By a ton

[full barn]

then what is angle X

[pure rapids]

We arent told

[full barn]

ahh i get it

[pure rapids]

Frfr

Now draw tangent

[full barn]

ok

i did

[pure rapids]

Put center

[full barn]

yeah

[pure rapids]

And draw OX

Then the angle to tangent is 90

[full barn]

ok ok

[pure rapids]

Since isoceles then OX passes through midpoint of PB so its also 90 then tangent parallel to PB

Finish

[full barn]

ok ok

tysm

[pure rapids]

Np

[full barn]

wait can you just explain why XPB and XBP are equal

[pure rapids]

Properties of Cyclic quad

[full barn]

the cyclic quad is APXB right?

[pure rapids]

Ya

[full barn]

alr alr i get it now

thx

[pure rapids]

Np

Bye!

[full barn]

bye

.close

[pearl pond]

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[floral knot]

isnt it meant to be 300

coz

[cosmic charm]

cos(300) is .5

[floral knot]

but

look i dont get it

[cosmic charm]

how do you know that distance gets you to 300

[floral knot]

i add 270 to 30

[cosmic charm]

yeah but on that graph

how do you know exactly that amount of distance gets you to exactly 300

[floral knot]

i dont know

i just just copy the same steps like i do for tan and sin and get the same value but seems like it wont work for cos

[floral knot]

i see

how come adding to 270 doesnt work

[cosmic charm]

why add 270?

[floral knot]

i meant as in

[floral knot]

lets say x = 30

one value is 30

next value is

360 - 30 = 330

[floral knot]

which will give you the two angles within the range

[cosmic charm]

uh huh

[floral knot]

am i unclear

[cosmic charm]

keep going

[floral knot]

ok so why cant i just do 270 + x

[cosmic charm]

why would you do that

[floral knot]

hmm acc i get it now ty

[pearl pond]

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[cedar trench]

im struggling to understand the solution of this probability qu

please could someone try explain a method

[cedar trench]

to this

.close

[pearl pond]

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[pearl pond]

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[sharp smelt]

Two real numbers $a$ and $b$ are equal iff for every real number $\varepsilon>0$ it follows that $\abs{a-b}<\varepsilon$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

We first prove that if $a$ and $b$ are equal, then $|a-b|< \varepsilon, \forall \varepsilon >0$
\
If $a=b$ , it then follows $a-b=0$.
\
$0< \varepsilon$ by definition
\
We're done

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[summer gorge]

yeah that looks good wai

[sharp smelt]

Thanks!

Also, hi!

[summer gorge]

hello

[limber oasis]

yeah this exercise is a no brainer

[sharp smelt]

We now prove if $\abs{a-b}<\varepsilon, \forall \epsilon >0$, then $a=b$
\
Let $a \neq b$. $\abs{a-b} =c$. But $\abs{a-b} < \varepsilon, \forall \varepsilon \in \R$. But $c \in \R$. A number can't be less than and equal to to a number at the same time. We've thus arrived at a contradiction

I think the inverval is overkill

just the fact that $\abs{a-b}=c$ is enough contradiction

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[tropic saddle]

|a-b| < a is not even true in general

[sharp smelt]

Typo

oops

[summer gorge]

this is enough tho

[sharp smelt]

Yeah

just realised IMO

[fringe raft]

but why is |a-b| positive?

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

Wdym

Is this fine?

[fringe raft]

epsilon must be positive

[summer gorge]

sure ig? I think just "but since c \in \bR we arrive at a contradiction"

but maybe I'm being too terse

[sharp smelt]

Right

Forgot to mention that

[sharp smelt]

Thanks

Eating now, so will close channel

.close

[pearl pond]

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[summer gorge]

bye have a nice time

[pearl pond]

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[static maple]

Hello

I need help with my Quantum mechanics task:
I have to calculate the energy eigenvalue and the "expected value" <E>

I really don't understand **how **to calculate the energy eigenvalue

• I don't know if I need to insert n, l & m in to psi and continue calculating with that (see picture 2)

Thanks in advance

[pearl pond]

@static maple Has your question been resolved?

[pearl pond]

@static maple Has your question been resolved?

[pearl pond]

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[bitter herald]

can a vector space exist without needing to equip it with the operations of addition between vector spaces and multiplication between a field and a vector space?

[bitter herald]

I never really understood if those operators are meant to be "auxiliary" in that sense

[tropic saddle]

those operations are what makes a vector space a vector space

a vector space is a set with those operations (and all the axioms)

[bitter herald]

I see that was a dumb question

is there a name for the subset of vector spaces that only defines addition between its members?

ok subset might not be an ideal choice of word

[tropic saddle]

there are things called groups which only have one operation

(and other things which also only have one operation but some other axioms)

you can basically say that the "additive part" of a vector space is an abelian group

i.e. the set with just the addition and forgetting the multiplication is an abelian group

[bitter herald]

That sounds pretty reasonable thanks

[bitter herald]

So, just a curious question, but would you suggest studying/learning about linear algebra from the viewpoint of an abstract algebra textbook if that makes sense? It seems to me to be a whole lot more "concrete", but my friend mysteriously also told me that it "might not always be the best of ideas" to do so, but I didn't really receive an elaboration from him on what's that supposed to mean

[tropic saddle]

I would suggest to first just start with a linear algebra book

abstract algebra books may assume that you know some linear algebra already

and even if not, they might need a bit more mathematical maturity

which you would gain from doing linear algebra first

[bitter herald]

It'a just a bit annoying sometimes that linear algebra books take a bunch of definitions for granted, outsourcing the explanation of those to an abstract algebra textbook

[tropic saddle]

what kind of definition are you talking about

[bitter herald]

Those textbooks don't tend to properly define what a field is, for example

[tropic saddle]

in some books you dont really need to know

cause you'll be working over just R and C anyway

which is why they dont give the strict def

there are obvious pros and cons to that approach

[bitter herald]

That's understandable in all honesty

I much prefer Tao's real analysis approach for example

He begins by teaching the Peano axioms and builds up the theory needed to actually perform "real analysis"

I much prefer delving into the basic form of what im dealing with. Something something better foundations

[tropic saddle]

you can definitely read for example the first few pages of the chapters in an abstract algebra book on groups, rings, fields

but not deeper

the kind of things the abstract algebra book will do with these structures afterwards isnt that relevant for linear algebra

[bitter herald]

Okay that might just be the best of both worlds then, thank you

I shall do that

[tropic saddle]

a lot of complications in for example group theory come from non commutative groups

the additive group of your vector space is always commutative, so you dont see those problems

you encounter them a tiny bit because matrices dont commute

but not so much more

at least on a first exposure. later you can always return with more knowledge of group theory and see some things from that perspective

which certainly can help but I wouldnt say its necessary initially

[bitter herald]

Alright, will keep in mind

Have a nice day

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[pearl pond]

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[pearl pond]

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[tame plume]

Residuals vs Fitted values

it doesent look like that its random right ?

[pearl pond]

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[pearl pond]

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[pearl pond]

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[stoic imp]

Let $S = { x \in \mathbb{R}^4 \mid 4x_1 + x_2 - x_4 = 0, , x_1 + x_3 = 0 }$ and $T = \langle (-1, 1, 0, 0), (4, 0, 1, 1) \rangle$. Find, if possible, a subspace $W$ of $\mathbb{R}^4$ such that the four conditions are satisfied:

\begin{itemize}
\item $W \subset S + T$,
\item $W \neq S + T$,
\item $W \cap S^\perp \neq { 0 }$,
\item $W \cap T^\perp \neq { 0 }$.
\end{itemize}

[jolly parrot]

xbz

[pearl pond]

@stoic imp Has your question been resolved?

[pearl pond]

@stoic imp Has your question been resolved?