serious-discussion

[lunar ruin]

Modify the steps such that you're not changing the rules, but working with a more manageable system. Then 1 or 2 even steps doesn't matter and you can just jump straight from the one odd to the next.

Then you don't need different rules each time depending on if it's even or odd. You can apply the same modified function each step

[light patrol]

I just don't think there's a way to condense the even step completely down into the odd without putting a conditional on it, which would still make it piecewise just in a different way

[lunar ruin]

I've done kinda already done it though?😅

[light patrol]

Oh?

[lunar ruin]

It's a bit complex though. So I can show what I mean by example. Pick a really huge odd number, then apply the steps like 20 times, then give me the first half of the digits in base 3. I can show you that I dont need to know if you took the odd or even steps. (Keep the old number for reference)

[light patrol]

1022122112

Reference number (don't peek, you're on the honor system here):
||973485613||

Side note while you're working base 3 is an interesting choice.

[lunar ruin]

Ok, so I'm giving the start of a number
10000111001110...
The above is x numbers above the current number. I'm gonna peak now

[light patrol]

(if it's wrong I probably hit a 2 instead of a 3 somewhere lol)

[lunar ruin]

base 3 helps with getting previous numbers in a sequence, and base 2 for how to move forward.

[light patrol]

Ahhhh

[lunar ruin]

Sorry if it's slow, I'm doing this by hand. Need to quickly check to see if I can find which node it was exactly.

[left fable]

Hey guys

[light patrol]

All good! I'm trying to find the base converter my friend made on desmos

Found it and I immediately saw the odd rule pattern for base 3

[lunar ruin]

I cant find the number you landed on. the number I gave might be higher in the sequence than the one you originally picked.

Think you needed to do a lot more steps 😅

[light patrol]

The reference number I gave was supposed be the starting number or after my 20?

Also I'm assuming your goal is base 3 on odds and base 2 on evens? That way it's one cohesive procedure and the piecewise aspect becomes the base conversion?

[lunar ruin]

The starting number is the reference number. Before you apply any steps

[light patrol]

Okay then I did that part right at least

I ended on another 9 digit also I gave front 5 in base 3 since that's more than half

[lunar ruin]

Nope. I dont know if the number is even or odd. Switching through bases in my function lets me skip that check. Though the number I end up with could be even or odd, but it doesn't matter because it's the same "node".

[lunar ruin]

Wait, so which number is this the start of?

[light patrol]

The end result?

[lunar ruin]

Of which number?

[light patrol]

Okay front half of the 20th iteration

[lunar ruin]

The 20th step: 259889290 is 200010000202002021?
I dont see 1022122112 anywhere there... 🤔

[light patrol]

OHHHHHH

I parsed before converting

I'm stupid

[lunar ruin]

Had me confused AF🤣

[light patrol]

I'm sorryyyyyy

I'm tiredddd

[lunar ruin]

Wanna try again? But like... 30 steps this time. Or pick any number of steps over 20. Now that we all know how the game works

[light patrol]

Sure!

102112222

Do you need the number of steps?

[lunar ruin]

Nope. Just need that.

[light patrol]

Okay
||775468243|| starting number

[lunar ruin]

101011110111 leads to...
10000011100111
Ok, lemme find them.

16 steps down. 552066749 in base 2:
100000111001111101111010111101
Matches my prediction:
10000011100111xxxx
And there's no way I could know whether you applied the even or odd rules or how many. But the pattern still works.

[light patrol]

Woah :0

[lunar ruin]

And the coolest thing? Can be done by hand 😁 (Getting the binary numbers that is. I used online converters afterwards to double check)

[light patrol]

That's amazing

[lunar ruin]

Glad someone appreciates it. I spent way too much time on collatz😆

[light patrol]

The thing is I've gotta see how it melds with what my friend and I have lol

Id rather not completely change but rather try and integrate things together. That way if there's an inconsistency it's either in wrong, the other guys wrong, or we solved the problem. XD

And if there's a bunch of consistencies and connections that leads to new discoveries most of the time

[lunar ruin]

What you guys are working on, is the pattern in the tail end of the number, but you're reliant on whether or not the number is even/odd. So it makes it complex having 2 rules to apply at different stages. I'm trying to find the patterns in the leading digits, which I've shown doesn't matter if it's even/odd, I can apply 1 rule each step

Maybe you'd want to try the same?

[light patrol]

Well the lagging digits determine the parity so if you're dealing with leading digits that means parity is going to inherently be meaningless to you

The lagging digits knowledge you have acquired might be beneficial in us figuring out more of the class mappings. Only thing we'll need to do is find a way to start from our seed rather than reach an endpoint

Because all in all the endpoint is the cycle

[lunar ruin]

Yip. Which just makes it so much easier to deal with

[tight goblet]

There are plenty of such books, although there is a considerable difference between "foundations" and "basics", in the way those words are usually understood :)
I'm not an expert in this area but when I was in grad school I did a reading project with some undergrads from Tomas Jech's Set Theory. It's a bit of a heavy lift at that level, I'll warn you, approaching the difficulty of baby Rudin.
That being said, depending on your interests it may not be so useful to be attached to ZFC as your axiom system. If you're really just interested in how to actually prove things super formally from axioms, you might be interested in the tutorial for Lean, called the Natural Numbers Game, where the interactivity makes it a lot more friendly IMO

EDIT: A probably better textbook rec was given by grass #book-recommendations message

[light patrol]

Best case scenario what we do is use the leading method to traverse but use the lagging method as like a broad coordinate system!

If we can find a connection between the two that is

[lunar ruin]

I can show you the connection if you want. DM me

[buoyant radish]

|x+1|>|3x-5|
when we square both sides do we have to flip sign

if so why

[rocky shuttle]

no

[buoyant radish]

oh then jus (x+1)^2-(3x-5)^2>0?

[strange mural]

How is Chaos Theory used in Mathematics?

[split basin]

its not

[strange mural]

Oh

It is used in Science, huh? Not Math?

[empty mirage]

Bifurcation theory is?

[empty mirage]

Old topic to my knowledge more physicists and stuff looked at it but there were some mathematicians

[strange mural]

Oh cool. Good to know. I was just asking because I remembered that the character Ian Malcolm from Jurassic Park was a Mathematician in the books, and he is famous for bringing up Chaos Theory to the general masses so I was curious about it.

[split basin]

dynamical systems is a topic in math

"chaos theory" is like a dogwhistle for pop sci gone wrong

[empty mirage]

I mean sure there is that side, but there is some dynamical systems stuff that got that term coined

[young ether]

are we moving here now

@uncut summit @empty mirage @split basin

[split basin]

yeah i think people initially hoped there would be a general theory of "chaos"

but it turns out to be ridiculously hard to say anything in general

[empty mirage]

I think there was some stuff that emerged as a result

[split basin]

for sure

[empty mirage]

Ergodicity Theory

[split basin]

that is much older

i think it's moreso stuff around smooth systems

[empty mirage]

Automata stuff

[split basin]

like systems of ODE

sure

[empty mirage]

Oh that I did not know

[split basin]

also fractals broadly construed

[split basin]

not ODE in general, that is much older

just saying those are the types of models people were focused on in the last ~third of the 20th century afaik

in dynamical systems in context of "chaos"

[empty mirage]

I really only know what was covered during my modelling classes

I wish to study more later once I have my own little diff geo framework for it

which I am slowly building

as a unification of certain desperately in need of working and being seen together areas of math 🥐

[split basin]

wot

[empty mirage]

But this is gonna take a while ;-;

[empty mirage]

I got projects that have to do with PDE and ODE which I wish to later use as springboards to turn to dynamical systems

but I need to get some diff geo stuff out the way first

in more words than necessary

I am but a pitiful barely grad ;-; I am le study

I am le work

[empty mirage]

To explain this comment, there are some areas of math I am interested in which are very deeply linked, in some cases the link is explicitly studied and in some cases no.

Which makes me want to study those from my perspective

make a bunch of links between these topics and get translations of various phenomena and this way get a way of talking about a bunch of things in a single

[empty mirage]

Here I point to the link between potential theory, laplacians, codifferentials and variational problems

Or dirichlet forms and the above in some other variant

This link is not the only one known to me, and some I only feel exist.

[solid yarrow]

Bushy :3

gang

[fresh comet]

[empty mirage]

fr fr

[empty mirage]

Foxy! 🥐 Hi!

[empty mirage]

Higher!

[fresh comet]

higher!

[sharp island]

HIgher

↘️

[empty mirage]

####HIGHER!

[fresh comet]

[sharp island]

Higher?

[fresh comet]

hello!

[robust laurel]

am ready for any integral equation or Diffeq

bring it on

[valid hornet]

Does anyone have a surjection from $\mathbb{R}$ to $\mathcal{P}(\mathbb{N})$? I know that $|\mathcal{P}(\mathbb{N})| \geq |\mathbb{R}|$ because $\mathbb{R}$ is defined as a subset of $\mathcal{P}(\mathbb{Q})$ which is equal in cardinality to $\mathcal{P}(\mathbb{N})$, but I'm having a harder time seeing the other way around.

[fathom swallow]

Heavenly Philosophy

[obtuse grail]

Hi

[light horizon]

Try thinking of elements of [0,1] as binary sequences

[novel tiger]

idk, i can somewhat think of a bijection from $[0,1]$ to $\mathcal{P}(\mathbb{N})$, and $[0,1]$ is homeomorphic to the extended reals

[fathom swallow]

Sapien

[valid hornet]

Well, that doesn't work because 0.011111... = 0.1000... So, do you represent 1/10 with the set corresponding to {1} or to {2,3,4...}?

If they map to both, then it's not a function.

[novel tiger]

Hmm

[valid hornet]

You could say that $f : \mathcal{P}(\mathbb{N}) \to \mathbb{R}$ a function that is surjective, but I already know that $|\mathcal{P}(\mathbb{N})| \geq |\mathbb{R}|$ for the previous reason.

[fathom swallow]

Heavenly Philosophy

[light horizon]

It works modulo countably many missing elements but this is ok

Because we can just take these from other places in R

[valid hornet]

So, we can take $f : \mathbb{R}[0,1]\setminus{\frac{1}{10^{n}} \in \mathbb{Q} : n \in \mathbb{N}} \to \mathbb{R}[0,1]$ as a bijective function?

[fathom swallow]

Heavenly Philosophy

[light horizon]

Is R[0,1] supposed to be [0,1] sub R?

[zealous garden]

The in Q is redundant

[valid hornet]

Okay.

Well, usually I'm thinking of the axiom schema of specification, so I like to define what it is a subset of.

[light horizon]

I mean certainly such a bijection exists but I was more thinking something along the lines of "let f be the map which takes x in [0,1] to the (non-cofinite) corresponding element of P(N), and then enumerate the cofinite elements of P(N) and map Z sub R to those"

[valid hornet]

Also, the 10 is in binary. I guess you could also replace it with 2.

[light horizon]

Actually, this brings up an easy improvement to my original thing

Just do it in ternary and there's no double counting

[valid hornet]

Okay, so it maps a subset of the reals to the entire powerset of the naturals? Since it's surjective, $|\mathcal{P}(\mathbb{N})| \leq |\mathbb{R}|$ is true. Thanks!

[fathom swallow]

Heavenly Philosophy

[valid hornet]

https://longformmath.com/real-analysis-book/real-analysis-hints-and-solutions/ The solution in 2.20 for finding a bijection doesn't work for this reason, which I find kind of annoying.

[vivid quest]

Niceeeee

Bijection from P(N) to R usually involve writing numbers in base 2

But that doesn't work because 2-adic numbers have 2 writings in base 2

Why

Why world why

Tho you can biject the almost constant sequences in the 2 adic

But like

Not as easy

[valid hornet]

But the surjection we found along with the fact that technically, $\mathbb{R} \subseteq \mathcal{P}(\mathbb{Q})$ along with the fact that $|\mathcal{P}(\mathbb{Q})| = |\mathcal{P}(\mathbb{N})|$ , we can get that the cardinalities are equal.

[fathom swallow]

Heavenly Philosophy

[vivid quest]

You can one shot a bijection i think

But ye this works too

[worthy shell]

man i havent thought of bijection between P(N) and R in so long

[vivid quest]

The idea i've seen before is that P(N) is bijective with {0,1}^N and those sequence basically write all real numbers in base 2

But it writes the ones with finite expression 2 times

Like 0.11111111...=1.0

[valid hornet]

It can get really confusing because $\mathbb{Q}$ can mean two different sets, technically. For example, if we construct $\mathbb{Q}$ as $\mathbb{Z} \times \mathbb{N}$, then how can it be the case that $\mathbb{N} \subset \mathbb{Q}$?

[fathom swallow]

Heavenly Philosophy

[vivid quest]

Q isn't exactly Z×N

[valid hornet]

For this point right here. I am referring to the construction of $\mathbb{R}$ from Dedikind cuts of $\mathbb{Q}$

[fathom swallow]

Heavenly Philosophy

[vivid quest]

Because 2/1=4/2

[vivid quest]

Oh right

You did it the hard way

Damn

[valid hornet]

Yeah, an equivilance relation is defined and all that.

[vivid quest]

So you construct R on top of proving it is in bijection with P(N)

Which is a lot more work loool

[worthy shell]

yeah i think you only take the ones with finite expression

[vivid quest]

No, you only take the ones with infinite expressions

[worthy shell]

like 0.1 would be allowed but not 0.011111... (actually this doesnt work immediately)

[vivid quest]

Yes ok

But idk how to biject that with P(N), what i wanted to do is to take them all and biject them the way i said but not the ones with almost constant expressions. The ones left we alternate them in a good way to biject them with the finite expression ones that were all left behind previously

Im just being a 🤓 for no reason here anyway

[valid hornet]

Well, as long as this original proof works, my curiosity have been resolved.

Finding an explicit bijection would be interesting nevertheless.

[vivid quest]

Indeed

[vivid quest]

Meant to reply to that

But ye direct bijections aren't always practical

[mint canopy]

Iirc it is independent of ZF that R and P(Q) have equal cardinalities, so an explicit bijection shouldn't exist, but I may be misremembering here.

Nevermind, this is in fact something provable in ZF

According to this MO post

[vivid quest]

Oh i really thought i had a direct bijection there

[mint canopy]

I was simply wrong

[vivid quest]

We could both be wrong

[valid hornet]

Well, since |N| = |Q|, |P(N)| = |P(Q)|. And from that Dedikind Cut construction earlier, R is a subset of P(Q). So, P(N) is at least as big as R.

[vivid quest]

How do you show the other way around?

That R is bigger than P(N)?

[valid hornet]

You have a surjective mapping from real numbers between zero and one that can be represented by 0's and 1's in a base larger than 2 (like base 10) to the powerset of the naturals in that way that we defined earlier. So, since a subset has a surjective mapping to the P(N), R is at least as big as P(N).

[vivid quest]

Okok

So that's the idea

Do you want more fun exercises about equipotence?

Because you basically just proved it

[valid hornet]

So, the problem of .1000... = .01111... doesn't matter because we're in a base other than base 2. That means that it's not a supposed bijection anymore, but we weren't looking for that, only a surjection, which we get.

[vivid quest]

Yepyep

So you just use another digit specially for some of them?

[valid hornet]

Sure. I was reading Chapter 2 of Real Analysis: A Long-Form Mathematics Textbook earlier, so I was thinking about some of the problems.

It's on cardinalities.

[vivid quest]

Wait i was trying to think of one that doesn't require much topology

It's not as easy as i thought

Ok i have one

What is the cardinality of $\mathbb{R}^\mathbb{Q}$

[fathom swallow]

almond 🐦

[vivid quest]

No mb

No ok that's it

That's one i thought about not long ago

It may or may not be hard

@valid hornet idk if you want hints

Maybe you already know it

[valid hornet]

Uh, I'm not sure what that's referring to. Is it referring to the vector space $\mathbb{R}^{\infty}$?

[fathom swallow]

Heavenly Philosophy

[vivid quest]

You can't just say that because infinite dimension can come with lany cardinality

But that's not the matter here anyways

Lemme explain

[worthy shell]

the cardinality of the set of functions f:Q -> R

[vivid quest]

Ok aristos said it

[valid hornet]

Oh. I see.

[vivid quest]

Do you have an intuition on that?

[valid hornet]

Well, my first thought is that a function is defined as a subset of the cartesian product. That probably is important.

[vivid quest]

Wym

[valid hornet]

Well, we can define $f : \mathbb{Q} \to \mathbb{R}$ as a subset of $\mathbb{Q} \times \mathbb{R}$

[fathom swallow]

Heavenly Philosophy

[vivid quest]

Oh i see

Wow i hadn't thought of that

It's way simpler than my 2 proofs

Wait no

My 1 proof

[valid hornet]

We can think of $\bigcup \mathbb{R}^\mathbb{Q} = \mathbb{Q} \times \mathbb{R}$.

[fathom swallow]

Heavenly Philosophy

[vast wraith]

[valid hornet]

But, some elements are duplicated. So, it might not preserve the cardinality.

[vivid quest]

Whaaaa

[vast wraith]

this does not make sense

[valid hornet]

Um, I mean the union of all of the elements in $\mathbb{R}^\mathbb{Q}$.

[fathom swallow]

Heavenly Philosophy

[vivid quest]

That's just R^Q lol

No your idea was very good, and imo that's it you've proven it

[vast wraith]

ah i guess that does work

[vast wraith]

it’s not

[vivid quest]

Oh

Oh

Im so dumb lmfao

Mistyping stuff on my end

[vast wraith]

we have the equality because for any (a,b) in Q x R there is some function f: Q -> R with f(a) = b and vice versa

[vivid quest]

You had it there btw

Almost

[vast wraith]

i dont really see how writing out this union is helpful though

[vivid quest]

I think we just need to let philosophy to have some time to think and all

I don't want to spoil them a result

And i think im confusing them more than anything

The cool thing with finding solutions to theses exercises it that they can be so various and original

I live that

You can almost make it an art lol

[zealous garden]

You what?

[valid hornet]

#serious-discussion message #serious-discussion message

[valid hornet]

Well, there is a mapping from $\mathbb{Q} \times \mathbb{R}$ to $\mathbb{R}^\mathbb{Q}$. In that $(q, r)$ can be represented by the function $y = qx + r$, so an injection exists. It's also the case that every function is a subset of $\mathbb{Q} \times \mathbb{R}$, so $\mathbb{R}^\mathbb{Q}$ is a subset of $\mathcal{P}(\mathbb{Q} \times \mathbb{R})$. So, $|\mathbb{Q} \times \mathbb{R}| \leq |\mathbb{R}^\mathbb{Q}| \leq |\mathcal{P}(\mathbb{Q} \times \mathbb{R})|$. I haven't had too much time to think about it. Also, the question is hard to answer because I need to interpret the question a bit more clearly. Should I have the cardinality in terms of aleph numbers or beth numbers or something like that? The chapter I read did not touch on those, so I am actually pretty unfamiliar with them.

[fathom swallow]

Heavenly Philosophy

[valid hornet]

We can't necessarily say that for any set $A$, there is a set $B$ such that $|A| < |B| < |\mathcal{P}(A)|$ because that would imply the continuum hypothesis. We also can't say that for any infinite set $A$, there is no set $B$ such that $|A| < |B| < |\mathcal{P}(A)|$ because that would imply the negation of the continuum hypothesis.

[fathom swallow]

Heavenly Philosophy

[quick beacon]

@valid hornet use beth numbers

aleph numbers require you to take a stand one way or another on the continuum hypothesis

other than aleph-null

whereas beth numbers have a concrete definition.

[warm umbra]

Welcome to the server @plush mirage

[plush mirage]

hello!

[warm umbra]

https://tenor.com/view/pingu-rising-from-water-hello-hi-waving-gif-5193317710960738776

[tropic pivot]

https://tenor.com/view/pingu-gif-3404514172503466945

[vivid quest]

By expressing it i meant compared to |N|, |R|, |P(R)|, and thing like that

If it was something like tye continuum hypothesis you couldn't express the set anyways

[vast wraith]

oh are we still doing this one

[burnt ledge]

R = P(N) = {0,1}^N so R^Q = ({0,1}^N)^Q
({0,1}^N)^Q = fns: Q to (fns: N to {0,1}) = fns: QxN to {0,1} = {0,1}^(QxN)
but QxN = N so ({0,1}^N)^Q = {0,1}^N = R

when i say = i only mean cardinalities are equal

just cba to write | • | everywhere

[vast wraith]

is (X^a)^b = X^(a x b) just currying?

[burnt ledge]

yes

[vast wraith]

lovely

[brave orchid]

pinguuuuuuuuuuu <333333

[cloud pewter]

Guys I need help

[brave orchid]

i used to watch a lot back in the day

[misty oracle]

@thorn jay That place is at the mid region of Taiwan

It’s a national park featuring marine lives

[empty mirage]

I have sent my current location

[neat lintel]

My brain is so cooked I thought mid region meant orthocentre 😭

[vivid quest]

Ok this is just op and destoying it

I see

This can be very useful

I never realized (A^B)^C is A^(BxC) before

But now that you say it

Yes

It works

Damnnn

I was so proud of my proof which now becomes useless

[wise bloom]

Hello

Wassup

[vivid quest]

I have used that so often without realizing it

[valid hornet]

One of the exercises in my book is proving that the set of real numbers algebraic over the rationals is countable. I think I came up with a proof last night.

It makes the most sense if I have an image to help visualize it, but I don't have image permissions in this channel.

I meant countable. Sorry.

[vivid quest]

It is indeed

What is the proof

I lean your proof

I can also show you my proof for R^Q if you want

[vast wraith]

i’d love to see it

[vivid quest]

Wait im in class so i'll wait to get to my puter

[valid hornet]

Is there a channel with image permissions I can put the visualization in?

I put the image here. #math-discussion message

Basically, sense we are dealing with finite linear combinations, the set of all polynomials with the ground field being the rationals is countable.

Only a top left square has any ones in it for each polynomial, so the sequence eventually is an infinite string of zeroes after some point. So, it corresponds to a rational.

[vast wraith]

i’ll check back later

[valid hornet]

That gets an injective function from $\mathscr{P}(\mathbb{Q})$ to $\mathbb{Q}$.

[fathom swallow]

Heavenly Philosophy

[valid hornet]

And there is definitely an injective function from $\mathbb{Q}$ to $\mathscr{P}(\mathbb{Q})$. You could just have each rational number $q$ correspond to $f(x) = qx$ as a polynomial.

[vivid quest]

Oh no

[fathom swallow]

Heavenly Philosophy

[vivid quest]

Impossible

Something has to be wrong

[valid hornet]

$\mathscr{P}(\mathbb{Q})$ refers to the set of polynomials with rational coefficients, not the powerset of the rationals

[fathom swallow]

Heavenly Philosophy

[vast wraith]

😭

[vivid quest]

What you were saying for polynomials seems right

But you can't inject P(Q) into Q

[valid hornet]

I would represent the powerset of the rationals as $\mathcal{P}(\mathbb{Q})$

[fathom swallow]

Heavenly Philosophy

[vast wraith]

please use the standard notation for polynomials over Q

namely

Q[x]

[valid hornet]

https://tex.stackexchange.com/questions/268072/symbol-for-set-of-all-polynomials-of-certain-degree

[vast wraith]

then it is true that |Q| = |Q[x]|

[valid hornet]

I just found this. So, I was going off of this.

[vivid quest]

Ohhhhh

[icy heron]

or just use Q[x] as notation for the power set of Q. Problem solved 😍

[vivid quest]

Lmao

Ok i get it now

[zealous garden]

ahem

2^Q

[vivid quest]

Something cool you could do to build f is that you can associate to aX^n the nth prime to the power of a, and say f(P+Q)=f(P)f(Q)

It's injective into N

And it's never infinite because those are finite

Also i think that's straight up a bijection with N*

[valid hornet]

Let $p : \mathbb{N} \to \mathbb{Q}[x]$ be a bijection from the naturals to the set of all polynomials with rational coefficients. Then, for a bijection from the naturals to the set of algebraic numbers, if $p(1)$ has $n$ roots, then assign numbers $1$ to $n$ with those roots. Then, assign the roots of the next polynomial of $p(2)$ to natural from $n + 1$ until its roots are reached. If you just keep doing, this all of the polynomials will be hit, because for each natural number $n$, $p(n)$'s roots will at most be $\sum_{i = 1}^{n - 1} r(p(i))$ places away, where $r(p(i))$ represents the number of roots of $p(i)$. Also, skip numbers if the number was already hit.

[fathom swallow]

Heavenly Philosophy

[haughty lion]

The set of exponential functions over Q

[vivid quest]

I might appreciate a theorem saying that a countable union of countable sets is countable

Which would have helped you conclude from the fact that Q[x] is countable

[gritty heath]

A polynomial is a finite tuple of coefficients in Q so one sees that Q[x] is thr union over all n of n-tuples in Q,
So |Q[x]| = sum_n |Q|^n which is countable

[valid hornet]

Well, the chapter I read on cardinality was pretty basic. It just gave a definition of the cardinality relations in terms of injections, surjections, and bijections, and then it proved that $|\mathbb{N}| = |\mathbb{Z}| = |\mathbb{Q}| < |\mathbb{R}|$. So, I have not learned about tuples or beth numbers or things like that.

[fathom swallow]

Heavenly Philosophy

[vast wraith]

here’s a nice thing you should try to prove: |N| = |N^2|

well this is the thing that underlies |N| = |Q|

[valid hornet]

Yeah. It's the same as the grid like structure in that proof.

[vast wraith]

the road from this to countable union of countable sets is also very short

[vivid quest]

A ye

I forgot about the basics lol

[valid hornet]

I have to be at class now. So, I'll think about it later.

[vast wraith]

fun fact the bijection N^2 -> N, counting along the anti-diagonals in that picture, is in fact a polynomial in Q[x,y]

it is even the ONLY known (up to reordering x and y) such polynomial bijection

[vivid quest]

Why do i have a feeling i can find another one

[thorn jay]

Was i pinged here

[thorn jay]

It looks so good

I am not used to such nice places

[lavish oyster]

Tf is this question lmfao

[quasi eagle]

Hello, ik this might sound like rlly simple question but I’m in hs rn and im still having misconceptions about simple maths. If y is directly proportional to x^2 then would it also be directly proportional to x? I wonder if it being linear vs square would influence proportionality 😅 asking before my quiz tmr lol. I’m guessing that proportionality is dependent on the equation?

Help this sounds so stupid I’ve asked ChatGPT 10 times

[granite delta]

could someone help me show that the function f(x) = x^3 - 3x is surjective

[fresh comet]

@lavish oyster welcome to the mathcord!

[lavish oyster]

Bruh why to tag me so late

[fresh comet]

try asking in a help channel (see #❓how-to-get-help)

(but as a hint: remember the definition of a surjection!)

[fresh comet]

because I'm not a bot

I'm a human who only just noticed your presence now, and wanted to welcome you

[lavish oyster]

That's basic math bro

[fresh comet]

please don't be condescending

what's basic to you isn't basic to everybody, and vice versa

let's treat everybody with respect, okay?

[lavish oyster]

Substitute c in it

Later

[fresh comet]

[granite delta]

My teacher just introduced me to functional equations.

[lavish oyster]

It's the onto and not onto functions right ?

x³ - 3x is a cubic polynomial

f(x) = y

Any cubic polynomial with real coefficient has atleast one real root

Therefore

x³- 3x - y = 0

So for every y belongs to R ( real numbers )

And there exists a x belongs to R so f(x) = y

You can atleast write the range right @granite delta

At the end
f(x) = x³ - 3x is surjective by R -->R

That's it

[granite delta]

thank for helping

[valid hornet]

This seems like it could happen if you had a choice function. Basically, one axis is $b_{1}, b_{2}, ...$ where $b_{n}$ is a bijection between $I_{n}$ and $\mathbb{N}$. The other axis is the natural numbers. So, the coordinate $(x,y)$ would correspond to $b_{x}(y)$. You could then do that diagonal thing like with the rational numbers. So, there would be a surjective mapping from the natural numbers to this infinite union. I think this requires the axiom of choice, though.

[fathom swallow]

Heavenly Philosophy

[valid hornet]

Or at least axiom of countable choice.

[valid hornet]

I'm thinking of a proof of the fact that if you have an injection from A to B and an injection from B to A, then you have a bijection from A to B.

[vivid quest]

I did not have time to go home and write my proof

https://tenor.com/view/cat-dance-cat-dance-gif-20491618

[fresh comet]

[warm umbra]

Welcome to the server @neat lintel

[neat lintel]

Heey, thank you!!

[mortal fulcrum]

Welcome to the server! 🙂

[neat lintel]

Thank youu!!

[torpid bay]

@warped pike we can talk here for more room

[warped pike]

ok

[torpid bay]

$f'(x) = \lim_{h\to0}{\frac{f(x+h)-f(x)}{h}$

[fathom swallow]

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

[torpid bay]

are you comfortable with limits or nah?

[zealous garden]

Calculus again?

https://tenor.com/view/here-we-go-again-gif-17983297559533351755

[torpid bay]

calculus to manifolds in 30 min time!

[zealous garden]

Based let's go

[torpid bay]

they aren't responding

[zealous garden]

Homie disappeared to go learn Calc 1->3 and pretend they aren't lost

[abstract cairn]

Hi just wondering what anyone thinks about propisitional logic or abstract math in school before uni.

[torpid bay]

propositional logic is good yeah

it's one of those things that you kinda learn at some point and need for the rest of uni

but 'abstract math' is a bit vague

[abstract cairn]

Originally I was thinking some basic stuff from something like abstract algebra. But Im not sure if that would be helpful. So maybe an intro to proofs class in highschool or something

[torpid bay]

intro to proofs, knowing a bit of intro set theory, a bit of linear algebra

[abstract cairn]

Oh to clarify I meant as part of a standard curriculum, not for myself specifically

[surreal bison]

frankly basic logic and set theory can and imo should be taught children along with algebra or arithmetic

[zealous garden]

This

Imo kids should learn abstract algebra instead of the quadratic equation

[surreal bison]

i mean set theory and basic logic are like... teachable in principle to literal 5 year olds

[zealous garden]

Yes

[gritty heath]

<@&268886789983436800> lets earn 100k in 72 hours

[zealous garden]

?

[zealous garden]

esta bien?

[agile fiber]

there was a crypto scam just now

[gritty heath]

Yea

[zealous garden]

oh I see, posted across multiple channels?

I thought I was in one where it had already been reported

[gritty heath]

Yeah multiple channels

[zealous garden]

Yeah I misread the series of events as

spammer
reported
more conversation
lol modping mentioning the thing reported minutes ago
I apollonius apologize

[torpid bay]

u cnahged pfp hunhh?

[zealous garden]

Changed the whole profile actually

[valid hornet]

For the life of me, I can't figure out a proof of the Cantor-Schröder-Bernstein Theorem. I don't want any hits, though. I'm just frustrated.

[storm sage]

That's a tough nut to crack

Fun one

[valid hornet]

I was showing a proof that the real numbers algebraic over the rationals are countable to a professor in office hours, and it implicitly used that theorem. And, he questioned me on that. So, now I want to prove that.

[gritty heath]

Yeah no worries, i was trying to be silly so its kinda my fault too

Was how it looked

[verbal quest]

what a Liam

[tropic pivot]

Noice

Please gift him a shiny boot for his deadliest efforts

[warm umbra]

Welcome to the server @pseudo ember @neat lintel

[pseudo ember]

thankyouu hii

[frozen burrow]

https://github.com/TruthIsHidden/Custom_Made_Cryptographically_Secure_Encryption_Algorithm

This algorithm achieved the highest byte entropy for its character set of 64 chars. 5.95 for a 256 char long input. (The theoretical max is 6) btw INSANE

[tacit storm]

Should i buy a Mac or Windows laptop for my degree in maths ?

[frail pasture]

Depends on what you need

If you just use LaTeX my m1 macbook air for one is just good enough

[tacit storm]

Well like programming

And latex for sure

[frail pasture]

If you just want to code python without using ml and ai then yeah it works, I use it for statistical stuff like R

if you want ml and ai then I cannot help you there while it works I doubt it can do that much crazy stuff, but then I'd rather you go for a desktop

[tacit storm]

I have a desktop

It’s a gaming pc

[frail pasture]

It's just the macbook air in terms of battery and performance it's just the best

Been using my M1 ever since release and it is a fanless device and all too

Battery lasts for days without charge using simpler stuff, and its power draw is not too bad in intense performance

[hallow plume]

i mean its just preference

[tacit storm]

Im looking more to a laptop i can use to learn python matlab etc ... rather than an actual beast

[hallow plume]

i use macbook air m3

[tacit storm]

Do you like it

[hallow plume]

yep

[frail pasture]

It does the job really

[hallow plume]

except that the cpu is too hot lmfao

[tacit storm]

Okk

Im looking for a m4

[frail pasture]

I mean if its intense stuff then yeah it gets hot

[tacit storm]

If i dont have any Apple device is that still like good ?

[frail pasture]

Just impressed it can still do well without a fan

[hallow plume]

idk

alternative way is that you get any other laptop than mac, and install linux

[frail pasture]

I tried that before but erm I cannot do that much command line lol

And when it has weird bugs I was kind of on my own reading how to fix it

So I moved to Mac because originally I was a Windows user then moved to Linux then moved to Mac lol

Never left Mac ever since

[tacit storm]

Im not an expert

Are there any thing you cant do on the Mac and frustrates you

Smth you can on windows

[hallow plume]

gaming

its extremely limited

[tacit storm]

Like what games

[frail pasture]

Yeah don't ever game with a mac

[tacit storm]

Do you want

It’s not made for that i guess

You can still buy an xbox serie s it does the job

[frail pasture]

Sure but it really depends on your preference really

I wanted to physically separate gaming and work so a macbook air works wonders for me

[tacit storm]

Yes i want that too

[frail pasture]

I do not want a lick of game in my mac so I went for that

[tacit storm]

Because with a gaming laptop ill be too distracted with gaming

Usually i play a lot

Unfortunately

[frail pasture]

Also gaming laptop has garbage battery life just saying :^)

So expect to bring a power brick with you

[tacit storm]

So i started to pretty much cut off games

[frail pasture]

Then why not a macbook air then? It has some of the stuff like linux and is well built

[tacit storm]

Im looking more into a windows laptop with good cpu and integrated graphics. 16gigs,1tb

[tacit storm]

256gb of stockage is sad

[frail pasture]

You sadly would need to pay a bit more

[tacit storm]

I expect 512 at the lesst

[frail pasture]

I went for 512gb and I feel is just enough for me, but I fear that's not the same for everyone else

[tacit storm]

Yes i see

I mean i can have a ssd external one

[hallow plume]

i use 256

because i have icloud stuff i dont need that much physical storage

[tacit storm]

Yea i can’t spend much on i cloud

And what’s the resell value on those macs

[hallow plume]

depends

[obtuse grail]

Hi

[frail pasture]

They don't drop off as bad compared to when the m1 was out almost all intel macs worth almost nothing when m1 got released

[tacit storm]

Okk

[polar temple]

all that specs with iGPU lol

[tacit storm]

Well yes

16gigs for programming i heard is enough

[polar temple]

yes 16gigs is great

i have 8gb sadly of ram

i can install more but i never did that b4

[tacit storm]

My brother installed 8gigs in his laptop

It was lagging

[polar temple]

what

is he doing for it to lag

maybe its his cpu/gpu not ram

most of the time, 8gb ram is sufficient

i have i5 U-series (13th gen) and 8gb ram

i didnt know U-series was one of the worse ones

my laptop is fine for most tasks but some development softwaare like android studio can get laggy

and obviously some games

[tacit storm]

Gaming

[round pecan]

apparently i made this txt file to crash applications idk

[frail pasture]

I never struggled with 8gb ram though

Then again I micro manage my software and all

I have only VSCode, Obsidian, Remarkable 2 Desktop app, and Librewolf

Oh and Racket and RStudio

MacOS

I thought we are talking about mac since Monest was considering it lol

My gaming PC is only linux because I am done with Windows

[polar temple]

i use windows 11 (unfortunately"

it's true that it uses a lot of ram but at the same time, a lot of that ram is just used to "not waste ram"

when you actually need that ram, it then frees up to use

[true zinc]

MacOS was originally based on an old version of NetBSD 4.2 which is where the mach kernel was born

[polar temple]

i'm purposefully being vague because i don't recall clearly

[true zinc]

We need 16-32GiB of RAM, 1TiB at-least of SSD space and preferably Linux to get our work done

and as our work involved generally running multiple instances of emulators to check software alongside physical devices

[polar temple]

what do you do?

[true zinc]

we kinda chew up RAM

like crazy

[polar temple]

that explains a lot

[true zinc]

emuldev (on our own time) and mobile app dev (where we emulate some devices as we don't have several phones on hand)

[polar temple]

i'm thinking about buying a new laptop once i get a job

either give this to one of my family members or sell it

i want a better laptop for development

[true zinc]

our current has a 12th gen laptop i7, 16GiB RAM and 512GiB storage so-

so so so limiting

[polar temple]

is this good enough if I install another 8GB RAM stick?

or should i get an i7?

[true zinc]

depends on your goals

[polar temple]

i want to be able to use apps like android studio smoothly

[true zinc]

we cause linux to trigger the OOM killer with just 2 instances of android studio emulation on 16GiB + 8 GiB Zram

[polar temple]

after the new update, it lags like hell for some reason

[true zinc]

so 16GiB may not be enough

[polar temple]

i just graduated high school so obv i wont be in craazy enterprise software development

im just a (former) student who is planning to go to uni at some point

i probably want to do a "maths + cs" joint course

[true zinc]

we got through basically all our uni courses with 16

[polar temple]

by the time i graduate, ill probably need to buy a new laptop anyway

[true zinc]

just fine

[true zinc]

Buy a laptop that's upgradable

and yes this limits you to....thinkpads and frameworks basically

back in the day every laptop was repairable and upgradable...mostly

[polar temple]

i kinda wouldnt mind games either 😭

[true zinc]

what types of games; we mainly play minecraft and osu and elite dangerous and this laptop can do that 100% fine

[polar temple]

ive never installed linux so im scared to

[true zinc]

it's very easy

[polar temple]

fairs

[true zinc]

@open umbra has radicalized us about them

[polar temple]

i am interested in using linux

i dont like windows 11

[true zinc]

me when void linux

is all I use

HELL YEAH

GENTOO IS SO GOOD

whyyyyy

just read the handbook

I've heard more horror stories with arch tbh

[polar temple]

not really sure tbh but i do plan to get minecraft

do u think i should just get 8GB RAM? and forget about getting a new laptop

[true zinc]

i5 13000 series U chip AFAIK with 8GiB

[polar temple]

.

[true zinc]

intel's chips recently have been quite shit

they run hot, have bad perf,and just

overall fuck intel

YEAH LMFAO

at-least they fixed that it seems

after gaslighting mobo manufacturers

[upper lotus]

nixos

i love nixos

install nixos

ull have fun

that was my first distro and it was very fun

[polar temple]

hm, that's nice

[upper lotus]

jump into the deep end and dont look back

i mean in the end its what you want to be able to do

[polar temple]

the thing is my laptop uses intel UHD graphics
but if i added another ram stick so that i have 2x8 GB then i would have dual channel memory which would allow me to use intel iris Xe graphics

which is probably better for games

would iris Xe improve the performance when playing games cuz im not exactly sure what the difference would be

i never installed ram before

[upper lotus]

also r u sure that the games u want to play are available on linux

[polar temple]

im scared to damage my laptop

then theres the thing about electrostatic discharge

which also scares me

[upper lotus]

oh i see

[polar temple]

honestly right now i want to play stuff like roblox, minecraft and wii games. but i do want to play other games once i can afford them

such as skyrim

which i can run ig

[upper lotus]

you can use wine for roblox i think

[polar temple]

a lot of games are off-putting

because they take like 80 GB of disk space

[upper lotus]

yeah you can get an external HDD

or SSD

idk why ud get an hdd in the modern era tho lmao

they're a bit cheaper

[frail pasture]

HDD is cheap and spinny bois are cheap

[polar temple]

well as long as i can develop projects fine without having a better cpu/gpu its probs fine

[upper lotus]

yeah tho if its only for like 500 gb you can get ssds for pretty cheap too

its only for like the massive sizes

like 10tb or something

where having a hdd becomes much cheaper

[frail pasture]

I use HDD for documents or off loading stuff

[polar temple]

cery?

[frail pasture]

SSDs for all the current stuff and all

[upper lotus]

if ur on windows u dont need to switch to linux to dev

but linux is nice

fr

[polar temple]

i think for modern games, u'll need a whole lot more

[upper lotus]

i can have my nixvim setup

[polar temple]

even if i had 1 TB, i can maybe download 10 games

[upper lotus]

yea i mean u can get up to like 2 tb for a solid price

[frail pasture]

Screw modern games they are all malwares at this stage lol

[upper lotus]

love my nixvim plugins

latex on nvim is fun

[frail pasture]

Actually I haven't played a game in 5 years really

[upper lotus]

nixvim?

[polar temple]

modern game companies must be working hands with storage disk companies nowadays

[upper lotus]

its a neovim distribution that you can get through a nix flake

and it makes configuring options for it super easy

[loud elk]

Whats harder Quantum Algebra or the Calculus

[upper lotus]

i have my configured nixvim on my github, so whenever i change something on my github and rebuild my configuration it just loads it from there

3rd person ive seen with a hollowknight pfp

one of them uses nix too

lmfoa

one of them is also the knight

the other one is grubs

ur grub is grubs?

[true zinc]

Nah just use linux for everything

it works well forthe most part

[upper lotus]

ik but theres not much motivation to switch for the average person to linux

u cant play valorant on linux

fr

[true zinc]

there is, it runs faster, your default web browser won't utterly torture you with AI ads, installing software via the terminal makes you at-leats a bit more vigilant to tracking what you do, updates are trivial on most distros aimed at average people, etc...

[upper lotus]

yea lmao

[upper lotus]

i mean default web browser isnt that deep you can just change it like i did to brave or arc or whatever you use
and what difference does it make whether you install it through the terminal or a website, neither gives you a guarantee you're installing something safe
I guess you know the name of it? but you can stop a download while it's downloading, and you can also see what file the download link leads to
updates are trivial on windows too

[true zinc]

Updates are trivial on windows for the most part but the maount oftimes I've had windows update break my setup is greater than the amount of times I've had dnf do the same; besides that, while you CAN change your browser many people just install chrome and follow the herd

[upper lotus]

i agree with runs faster but to be honest i dont need my computer to run faster in basic tasks since it's got more than enough processing power for basic tasks
i guess depending on the quality of your computer you might have more incentive to just run a linux minimal install atp

[loud elk]

Guys can i do hack the box or CTF in windows like Windows 10 like fr Windows 10

[upper lotus]

uhhh

i think so

you can use WSL

for any linux commands you need to do

for something like that people prefer kali or smth

[loud elk]

How to set wsl

[upper lotus]

this is one of those things where you would benefit from searching it up

i think you can just type wsl in the powershell tho lol

and itll run an install if you dont have it alr

[true zinc]

RTFM

(read the fucking manual)

[upper lotus]

or wsl --install or smth

[upper lotus]

fr

[true zinc]

https://learn.microsoft.com/en-us/windows/wsl/install

[upper lotus]

read the fortnite manual

[true zinc]

I'm usually very "politically correct" or whatever but sometimes a bit of crassness is necessary

fair fair

[upper lotus]

bruh

i hate when i hit the next button on a survey

and it just auto submits

[loud elk]

How about without wsl can i do it?

[true zinc]

not really

[loud elk]

Can i love her without a manual book

[true zinc]

I think this is heresy

you should appreciate the need to read documentation

it keeps you smart

-Ryan

[loud elk]

Can i be with her even if that means death

Actually

🤓

[upper lotus]

wait

what's the probability that james responds

instead of ryan

[true zinc]

Normally I'm the one who does tech stuff in our system, but Ryan's really good at being a bit of an asshole (and also knows way more maths than I do)

[loud elk]

Death is blah blah blah blah blaha blah blah so you cant be wither forever because mimimimmimimsuskos

[true zinc]

so I let her front when I'm really irritated

-James

[upper lotus]

what do you do while she does that

do you eat to suppress your rage

do you eat nachos

[zealous garden]

Advising people on how to use WSL when you should be advising them on how to switch to Linux outright

I'm ashamed

[true zinc]

no normally I'm partially forced out of our consciousness and I can only watch

me when cofronting

[upper lotus]

im on some massive cope shit
i got my wisdom teeth removed last wednesday and i cant stop thinking about solid food

[true zinc]

It does not seem some of these people would enjoy a direct drop into the deep end tbh

[upper lotus]

they asked if they can keep using windows

and lowk fuck VMs

[zealous garden]

What are you talking about

Bare metal

[upper lotus]

like i'd rather use WSL than virtualbox

no i know but like if they want to keep using windows

they can use WSL

lowk yeah

[zealous garden]

I run windows inside qemu on my Linux installation

This is the proper way

[upper lotus]

they could do with arch linux

or redhat

lowk just switch to linux fully

and dont ask anyone for help

then you'll never need to ask someone how to install wsl again

[true zinc]

one should ask for help at times

[upper lotus]

yeah sure when they exhaust all other reasonable options

[true zinc]

but stackoverflow, unix SE, archwiki, gentoo docs, and rhel docs are SO good

I got into linux already having read all of these soruces EXTENSIVELY

like I'd read them for about a year before I actually ever installed linux

[zealous garden]

This

[true zinc]

even today sometimes I do need to open the docs to find something I need that I don't do frequently

[upper lotus]

i think if the docs r outdated then u can ask for help
cuz the nixwiki is lowk worthless

the majority of the time i have to go onto the nixos github

and read source files

[true zinc]

also learn to use the system man pages

especially for C and shell

[upper lotus]

cuz shit can be outdated in the wiki

[upper lotus]

and this is such a nuisance

but i have someone i can ask about nix so i just do that for really big things that would take hours and hours of scouring through

[true zinc]

To me this is just a trial by fire

you get used to it

and you become self reliant

[upper lotus]

someone else already did so i dont have to 💔

i dont want to get used to reading their code

file after file

[polar temple]

default web browser
like anyone uses microsoft edge on windows

[upper lotus]

looking for examples and ways in which they use certain syntax to try to understand it

and trying to find where a specific command was created

i think you can just pay for it without selling a kidney

but fr i think its just expensive

i dont think theres much you ca really do about that

maybe you can find some parts off of marketplace

😭

i wish i never have to get a job again

im investing everything in a 10 cent market cap pharmaceutical company

yes

i mean thats how it should be anyway fr

invest everything

who needs liquid cash

[old oak]

That's complicated and boring though, much more exciting to yolo everything into a penny stock or a memecoin

In reality I keep my assets in an assortment of actual stocks, bonds, and index funds; but I'm a very boring person.

[upper lotus]

no just joking lol

[lunar ruin]

That's cost a total of around 10 cents to own the entire company. Hope you're up for such a huge risk

[wet quarry]

aint no way job is being censored here

[upper lotus]

it is a huge risk

it's everything i have

[wanton roost]

Hey guys

Can anyone help me out with a few questions regarding studying math in uni?

[ocean harbor]

!da2a

[quasi jetty]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[wanton roost]

Ok

Thank you

I've been trying to decide between pursuing medicine or doing a double major of Math + Computer science.
Does anyone have any tips or words of advice for me?

[wet quarry]

math + cs is a good combo, it just depends on if you can manage doing a doube bachelor

[wanton roost]

do u think a master's degree would be necessary after?

[wet quarry]

depends on your echonomy, i definitely dont think that a master or even a double bachelor is necessary to land a well paying job.

[polar temple]

how passionate are you about medicine?

medicine is a really hard field to get into

over here, it's more likely to enter on the second year of application

do you mind if i ask what country you're from?

[fresh comet]

[wanton roost]

I love biology and chem, my original plan was to study med

[wanton roost]

spain

i've been living here for 7y

[polar temple]

how come you started going for cs+maths?

is it possible for you to apply to both and see what happens?

[wanton roost]

Math's always been a passion of mine. Also my sister's boyfriend finished his math degree and his master's in data analysis and he showed me what he studies and what job offers he got when he finished and i thought it was awesome lol

also it's way less time than medicine

[polar temple]

that's cool

[wanton roost]

Not rlly because in this school year I have to choose between physics and biology

[polar temple]

medicine is very stressful

and a lot of people who pick medicine end up dropping out bc they realise the pressure of the work environment is too much for them

not saying dont do med

[polar temple]

ohh

are you 16 or something?

maybe try researching each field more

[wanton roost]

and when I choose to do the final year exams ( equivalent to the SATS ) I would have to choose between doing physics or biology too. And depending on the uni degree if you do biology your "admission grade" gets a 0.2 weighting factor

[polar temple]

if you graduated with medicine or graduated with maths+cs, which careers would you be most interested in?

if you

if you're smart enough, maybe try picking extra subjects?

[wanton roost]

yea

[wanton roost]

im in my last year of school, 17 turning 18

[wanton roost]

if I graduate medicine then i'd do residency in the US, probably radiology, dermatology, ophtamology or orthopedic surgery

If i graduate math+cs maybe a quant or a data scientist ( im kinda new to the whole computer science stuff )

software engineer or cybersecurity would be nice

[polar temple]

hmm interesting

[wanton roost]

You know what I'm afraid of?
doing medicine and regretting not doing math+cs
also afraid of doing math+cs and regretting not doing medicine

[polar temple]

yeah

thats problematic

[wanton roost]

btw here math+cs takes 5 years and medicine takes 6 years

[polar temple]

ive known a lot of people being rejected from medicine. of course, you could be different to them.
ive known a smart person who received AAAA (not sure his predicteds) and was rejected from medicine.
he picked engineering as a backup so now hes going to start doing that.
(im in england so most people pick 3 a levels but he did 4: maths phys chem bio)

im not sure if this is even relevant to say but even if you pursued medicine and unfortunately did get rejected, do you think its possible to sit another qualification for physics privately to pursue maths+cs afterwards?

do u actually need physics to apply to maths+cs?

is it just more competitive than bio?

[polar temple]

wtf

5 years

why

here, maths+cs is only 3 years

and medicine is still 6 years

here, its more like a 50/50 split in modules

is it different for u?

[wanton roost]

it would be possible but i'd have to wait a year ( and learn this year's physics by myself )

[polar temple]

well as long as u have no regrets, nothing wrong with having to wait a year i think?

[wanton roost]

cuz its a double major so u get both degrees

[wanton roost]

thats so good whatttttt

[wanton roost]

It depends on the Uni tbh

[polar temple]

we dont really have majors and minors in england

[wanton roost]

yea ig

[polar temple]

surely there's a lot of resources online? not sure about your curriculum tho

but self-learning can be hard, yes

[wanton roost]

there r yeah
I think i could do it, the only downside would be the ""time wasted""

But oh well I still have like 1-2 weeks to think about it

[polar temple]

i can understand

im lucky to have not been in this situation

yeah, take that time to think carefully

[wanton roost]

R u in uni rn?

[polar temple]

and research more about the fields

no

[wanton roost]

Bet

[polar temple]

i just finished high school

[wanton roost]

Oh nice

what r u gonna study

[polar temple]

a lot of my classmates will start uni soon

but im not

here, we have a strange system of applying with our predicted grades

and i didn't like mine so i grinded for better final grades

so i'll have to join uni a year late (but honestly, ill probably apply for 2027 entry cuz of finances)

and im thinking of applying for maths+cs

in durham

[wanton roost]

I see

[wanton roost]

Best of luck man

[polar temple]

im a little disappointed in my final grades but theyre not bad grades

i just wanted to go to another uni

[wanton roost]

I have a friend who's from there

[polar temple]

that wanted higher grades

[wanton roost]

Ic

[polar temple]

i was predicted BBD and finished with A*AB but I needed A*AA for the uni i originally wanted to go to

but A*AB is still a good grade

[wanton roost]

A* is like the max right?

[polar temple]

thats cool

yeah

[wanton roost]

That's rlly good

[polar temple]

A* A B C D E U

[wanton roost]

which subjects did u pick?

[polar temple]

U is basically a fail

but C is the standard pass for uni entries

[wanton roost]

I've seen a guy on tiktok who got all Us lol

[polar temple]

i did maths, further maths, computer science

for a levels

[wanton roost]

awesome

btw

my sister's bf who finished math and did a master's degree on data analysis is looking for a job rn

he's been looking for like 1 month

[polar temple]

the job market is hard rn

[wanton roost]

and he's been taking hella interviews because he wants something very specific, he wants a job abroad that also will allow him to work remotely in the future

[polar temple]

i hope it goes well for him

[wanton roost]

he also told me that some contractors will just outright not hire anyone who hasn't studied in a very well known uni like harvard or MIT lol

[wanton roost]

me too, he's a good guy

[wanton roost]

Do u think computer science is cooked rn is there still hope

[polar temple]

i have a classmate who is joining durham maths this year

so if i do go durham, its cool ill probs get to see him

[polar temple]

hmm the field is quite saturated and im not an expert on the job market

but thats why i want to go to a really good unia

and get a first class honours in my degree

and build a portfolio and hone my skills outside class

[wanton roost]

thats nice

here in spain the Unis are not ranked very high globally

[polar temple]

im sure there are unis in spain that are ranked highly in spain

[wanton roost]

the best unis here are ranked in the top 100-200

[wanton roost]

yea

[wanton roost]

the best one is in barcelona, its ranked 130 or smth

[polar temple]

i mean in national rankings

theres unis in the top 10 rankings in england but i dont think some of them are in the top 100 globally

so companies abroad might not recognise them so much

but companies in england definitely will

[wanton roost]

u got Imperial College London there tho right

[polar temple]

kind of like how there are good unis in each state in the US and companies do know these unis

and people in the US know these unis

but i dont

[wanton roost]

yeah thats my fear for me

[wanton roost]

yh

[polar temple]

most people in england dont know unis in the US besides ivy league

companies might idk

[polar temple]

thats a crazy uni here

[faint light]

come bath maths rahhhh!!!!

[wanton roost]

US is stacked with ivy leagues ts is crazy

[polar temple]

i wanted to go to bath for cs

[wanton roost]

yea

[faint light]

ohh cs not maths

[polar temple]

i was obsessed with getting an A* in fm

so i narrowly missed my A in cs

[faint light]

i had an imperial offer but rlly wanna go

[wanton roost]

That's why it's very important to build a portfolio I think

[polar temple]

i was 7 marks below an A* in fm

and i was 4 (scaled) marks below an A in cs but after a remark, i dropped 2 more marks 💀

[faint light]

i was very close to an A*, so annoying cause i missed my firm bc of it

[wanton roost]

Even if your school is not in the top 50s atleast u have a portfolio

[wanton roost]

why

2nd best uni in the world

nvm i read " dont really wanna go"

[polar temple]

imperial wants 3A* for cs

[faint light]

didn’t really care for it much, london is expensive, wanted to be in a new city, etc

[wanton roost]

crazyy

[polar temple]

but im contextuals so they might take A*A*A

[wanton roost]

ic

[polar temple]

which i didnt get

[polar temple]

i like maths which is why im thinking of picking maths+cs

[wanton roost]

you guy's system is so different from ours

[polar temple]

its just that maths careers dont seem as fun

[wanton roost]

ours is more complicated

[polar temple]

what year was this?

[faint light]

2024, 86% was an A* and i got 84%

[polar temple]

damn

what exam board

2025 was worse than 2024 imo

[faint light]

Edexcel

[polar temple]

what modules

[faint light]

FS1 FM1

[polar temple]

i did FM1 and D1

this year we had 62/75 in CP1 for A*

70 in CP2 for A*

FM1 had 72

[faint light]

longggg yeah ours was similar

[polar temple]

D1 was 53 but thats the worst paper i ever sat (but d1 is the easiest module)

72 out of 75 is batshit crazy

craszy i got 73 tho

[faint light]

FP1 was 72 in our year

[polar temple]

i couldnt believe it at first

because i dont even do physics

reddit answers had me thinking i got mid 60s

in fm1

ig it was a somewhat easy paper but i didnt think it deserved 72

[polar temple]

yea ik

62, 70, 72, 53 for A*
and i got 61, 62, 73, 54

😭

cp2 fumbled me

[wanton roost]

LOL

Every year the uni admission exams here get leaked

And they have to change it

🥀

[valid hornet]

Now I'm thinking of how to prove that between any two sets $A$ and $B$, there exists a surjection from $A$ to $B$ or an injection from $A$ to $B$.

[fathom swallow]

Heavenly Philosophy

[valid hornet]

That would complete it.

[burnt ledge]

What are you completing out of curiosity @valid hornet

[valid hornet]

I mental challenge.

[burnt ledge]

Also, How did you prove cantor schroder bernstein?

[valid hornet]

I'm just trying to do it to see if I can, honestly.

[valid hornet]

Well, I need that piece to prove it.

But basically, you could restrict the domain of the second injection to the range of the first one. Then, you restrict the codomain of the second injection to be it's range so it's a bijection. Connect the two bijections to form one bijection. Then, you have $A \subseteq B \subseteq C$, where $|A| = |C|$. Then, you would have a disjuctive syllogism with either $|A| < |B|$, $|A| > |B|$, or $|A| = |B|$.

[fathom swallow]

Heavenly Philosophy

[valid hornet]

The first two in the disjuction are false, so the third must be true.

So, we have injections $f : A \to B$ and $g : B \to A$. We then can restrict it to $f^{} : A \to \operatorname{range}(f)$ to get a bijection. Then, we get $g^{} : \operatorname{range}(f) \to \operatorname{range}(g)$ and then restrict $g^{}$ to get $g^{**} : \operatorname{range}(f) \to \operatorname{range}(g^{})$ to get another bijection and then connect them.

I don't know the range symbol.

No, I need to fix something.