Let's post (very) hard problems of our fields of study, but using images like this one that pretends it's actually easy

Sorry guys, the first version wasn't hard but impossible to those who don't assume all topological spaces to be Hausdorff or atleast T1 by default.

take the two points x, y
use the fact that there exists a continuous function f:X-> [0,1] with f(x)=0, f(y)=1
but if it's continuous then all values between 0 and 1 must appear for some argument
so X is uncountable

This is the equation for the oscillation of a simple pendulum, you should be able to solve this.

[eqn]\frac{d^2}{dt^2} \phi + \frac{g}{L} \sin \phi = 0[/eqn]

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It's - 12 dumbass

And "efficient" means something better than the naive one that first comes into mind.

CS fag

Space is normal -> space is T1 -> all singletons are closed
Atleast two points -> two disjoint closed sets
Space is normal -> space is T4 -> Urysohn's lemma -> there exists a continuous map taking one singleton to 0 and the other to 1
Space connected -> the image is connected -> the image is the uncountable closed unit interval
The cardinality of the image is at most the cardinality of the domain -> X is uncountable

countability is a retarded notion in constructive math

calm down, wily burger
let the heathens have their degenerate fun

That's just excusing your laziness using fancy words.

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1/3

2/3
not a problem per se, but with animu girl

3/3 eh

>God writes out the entire standard model Lagrangian just to create light
>doesn't know that the QED Lagrangian can be written with less than one line
>puts complicated looking formulas where they don't belong
Yeah it's made by a Christcuck alright.

The inverse images are points [math]2\pi[/math] apart. Also the word "fibres" should be reserved for cases where [math]\phi^{-1}(m)[/math] is uncountable for each [math]m \in H[/math].

>they think I have any idea about these solutions
>tfw I'm a chemfag actually
pic familiar

>Doesn't understand the appeal of a single Theory of Everything
>666

>solutions
Only one of the three you posted was even a problem. I know you're a chemfag, but you can't be this dense.

>implying God would waste his time writing down all that shit just to say "let there be light"
God is a Pajeet who doesn't understand computational efficiency?

>'twas merely an act

Fuck off, Satan.

Here's another.

You're assuming path-connectedness, not connectedness.

4/3
I managed to find some more in my fapfolders

5/3
there's something very amusing about combination of animay girls and scientific mumbo-jumbo

6/3
well, that's all I got for now which is anyhow relevant

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That's a pullback!

If we can have different kinds of infinity why can't we have numbers with infinitesimal components?

You can but that's not [math]\mathbb{R}[/math]

Math wankers have to atleast admit that they like to say simple shit with complex language

Is it possible to use chords to divide a circle into equal area pieces with no two pieces congruent?

This one wins

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>muh non-small angle approximation
>muh elliptic integrals

:^)

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Not a day goes by where I don't wish I was a stronger and more confident person in life. Keep studying kids even on this fine Saturday night.

Elliptic curves provide the basis for some real-world cryptography and algorithms for factoring integers.

lol that's just silly. what would curves have anything to do with integers? XD

lol why should i care about this mental masterbation with no practical utility

>no practical utility

>cryptography

Did you even read the post, faggot? Do you legitimately not know what cryptography is?

To make this conversation better, wordfilter each instance of "integer" to "nigger".

I have a math degree and I legitimately cannot tell if this is gibberish or a real question

>quantum field theory
Yep, it's gibberish.

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>You should be able to solve this.

I have a lot of these saved up.

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you were never introduced to the concept of elliptic curves

>Math is the least flawed of any human construct.
FTFY

For funzies

(You)
I couldn't find much of these, so made one myself

>tfw you will never have a qt anime grill read you a bedtime stem textbook
why haven't i an heroed yet mina?

cont'd
7

8

9

10
aaand once more I'm done for now

Wait. If p is prime doesn't that imply that the square root of p is always irrational?

If so how are you going to work in the rational numbers?

Okay, nevermind. You probably mean that the coefficients of the vectors can only be rationals.

See, but limx->(inf) of (1/10^(x)) is a limit. There's no point where (1/10^(x)) is actually zero. And 1-(1/10^(x)) is never equal to 1

to be a pullback square, S must be a pullback and everything must commute
so S must be a subset of the product of X and 1 such that for some x in that product, phi(x) = true
(the product of X and 1 is essentially just X, which allows for this sort of abuse of notation)
assuming i is the inclusion map
phi.i:S->2 is always true, because the codomain of i is exactly S, and phi is true for elements of S
this makes S a pullback and makes the diagram commute

and there's no point where 0.999... is anything but 1

But there is a point where 1-(1/10^(x))=0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 and even more nines. To infinity at some point. But never really 1. So?

fyi problem of 0.99.... =1? emerges only when flawed decimal notatoion is used, in base 12 there's no such problems, although there may be conundrum of similar kind dividing by, say, seven, which again in a different base doesn't yield recurring notations

Yeah, and that point is 1.

1=1-(1/10^(x))
(1/10^(x))=0
Solve for x

>he didn't learn limit theory
kys

I bet you are Zeno's """"paradox"""" defender too

A limit is not necessarily the value of a function. It's what the function approaches. Try again

The Achilles one? The theory might work but in reality that's not how shit works

>value of function
ofc it's not, given a definition of a function
the number here discussed can be defined through previously mentioned function, where actual value is defined as a limit of that function

>Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.
Pasta

also acceptable
>characteristic function is subobject classifier in Set
>QED

The Galois group of Q adjoin finitely many square roots of primes is isomorphic to (number of sq of primes) copies of Z/2Z.

Use the primer number theorem

It's not a proof if you use a result of the same order of difficulty without proof (although that will work). You might as well be saying "it's true, because it's true"

Nice alteration of the pasta

>Also the word "fibres" should be reserved for cases where ϕ−1(m) is uncountable
This is absolutely not the case.

why don't we just use a base that is the product of all the basic numbers (1, 2, 3, 4, 5, 6, 7, 8, 9 and 10) then? we could divide everything without nasty results

>he thinks product of 1 through 10 is sufficient
nah dog, multiple-digit primes exist and there's infinitely many of them
to be able to divide freely we'd need a base that is a product of all primes, which is improssible, OR we could use fractions for rational numbers that are found recurring in attempt to present them in decimal, that is with dot or comma, notation.

Alright, the extensions over Q will be of degree at most 2^n as it is a composition of n extensions of degree 2.
Its Galois group contains automorphisms fixing all square roots of primes except for one that goes to minus itself. Hence the Galois group contains the group generated by all those autos which is isomorphic to n copies of Z/2Z.

But by degree considerations we found what the Galois group should be. Thus, a Q basis for the extension is given by the square root of product of primes, which gives Q-linear independence

Newfag here and I wanna say you are hilarious, finding AT and AG problems on funpost make me laugh as fuck.

You're still implicitly assuming that none of these extensions "collapse." For instance, it is not a priori obvious that [math]sqrt 3 \not \in \mathbb Q \left( \sqrt 2 \right)[/math]

the fact that we still cannot analitically solve for the motion of something so simple as pendulum really makes you think.

on that note, the fact that you cannot solve for something as simple as the motion of a diatomic molecule without resorting to approximations also really make you think once you consider the real world (don't get me started on the universe) is made of extremely complex molecular and atomic structures.

physics is all about symmetries and approximations, and that's the best we can do.