/mg/ math general: LMFDB edition

Euler's theorem, and then since if p is odd, p-1 even, so there is a square root of 1 which is -1, because otherwise the order would be too small.

Show that 3/2 > 1, and that the left hand changes by a factor higher than 1 each n, and the right hand changes by exactly 1, so therefore the LHS must stay larger.

Thanks I didn’t see it said that too.

Thanks I read en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Geometric_meaning and I understand it better now!

Can we agree this proof is shit? In (ii) there is no reason for W(a) != S.

Glossary: I is the set of ideals, W(a) is the initial interval determined by a.

Dugundji's topology btw.

>usage of classical logic
>Can we agree this proof is shit?
Absolutely.

Can anyone give me an example of two metrics which induce the same topology but are not equivalent?
Wikipedia claims this is possible but doesn't give an example.

Inducing the same topology is by definition being equivalent. Do you mean that inequality using two constants? If so I have a tip: boundness of a metric is not an equivalence invariant.

>muh constructionism
Let the big boys talk.

>muh
>constructionism
Way to expose your newness.

ESL m8.

Disbelief.

>Way to expose your newness.
Oh, the irony...

This makes no sense in context. Are you mentally ill?

>This makes no sense in context. Are you mentally ill?
It makes perfect sense in context. Are you mentally ill?

How truly pathetic.
*yawn*

Which part of the irony confused you?

Maybe you are confused.

>Maybe you are confused.
It's possible, but I doubt it.

Meanwhile it's very clear your 'newness' comment was hilariously ironic.

You are daydreaming.

>You are daydreaming.
How so?

Unlock your heart, user.

>Unlock your heart, user.
What do you mean?

A-user, I...

>A-user, I...
Are you ok?

Why are you stuttering?

Stop bickering and answer me faggots. Am I crazy or Dugundji can actually make mistakes?

>faggots
Why the homophobia?

Too much Veeky Forums user, I'm sorry for your feelings.

Nvm, fixed the proof, Dugundji was lazy as fuck. If you are in the (ii) case then $S=W(b) = \cup_{a

...

>What about reddit?

huh?

It's your home.

>It's your home.
What do you mean?

might be time to consider this has more to do with your personal experience. Clearly there are many people who do active research in it, even in major branches of math. I know some people from JHU, and they have a very active CT community, almost entirely applied (number theory, homotopy theory, geometry, etc.). All the people I met from there were very familiar with CT (Emily Riehl is there), but also with their field of study, and understood the importance of both moving forward.

Don't let the CS fanboys who've only read Awodey ruin a great tool and field for you.

I'm trying to define some basic algebra concepts in Category Theory but I'm running into trouble with formalisms.

The category Set is defined as usual:
Objects: sets
Morphisms: set functions

If [math]G[/math] is a group then we can define it as a category [math]\mathcal{G}[/math]:
Objects: Single object [math]G[/math]
Morphisms: [math]g:G\to G[/math] for each group element so that the identity element is the identity morphisms on [math]G[/math] and composition is (right) multiplication in the group and all morphisms are isomorphisms (yielding inverses).

Note that [math]\mathrm{Aut}_\mathcal{G}(G)[/math] yields our group under composition.

Let [math]\mathcal{U}:\mathcal{G}\to\mathrm{Set}[/math] be the functor that sends the group to its underlying set in the category [math]\mathrm{Set}[/math].

A group action where [math]G[/math] acts on a set [math]R[/math] is defined as a functor
[math]\mathcal{A}:\mathcal{G}\to\mathrm{Set}[/math]
[math]\mathcal{A}:G\mapsto R[/math]
[math]\mathcal{A}:g\mapsto f[/math] where [math]f\in \mathrm{Aut}_\mathrm{Set}(R)[/math]

Note: Automorphisms on a set are permutations. So [math]\mathrm{Aut}_\mathrm{Set}(R)
[/math] yields the symmetric group [math]S_{|R|}[/math] under composition.

A group action where [math]G[/math] acts on itself is defined as a functor
[math]\mathcal{A}:\mathcal{G}\to\mathrm{Set}[/math]
[math]\mathcal{A}:G\mapsto\mathcal{U}(G)[/math]
[math]\mathcal{A}:g\mapsto f[/math] where [math]f\in \mathrm{Aut}_\mathrm{Set}(\mathcal{U}(G))[/math]

For instance, the group [math]S_3[/math] acting on itself is analogous to taking [math]S_3[/math] and embedding it in [math]S_6[/math] (since [math]S_3[/math] has [math]6[/math] elements then [math]\mathrm{Aut}_\mathrm{Set}(\mathcal{U}(S_3))[/math] is [math]S_6[/math] under composition). Unfortunately, this makes it difficult to define an action that does conjugation (as it would require multiplying elements of [math]S_3[/math] with elements of [math]S_6[/math]). Any help?

let d a metric

define a new metric d' = d/(1+d)

Same topology, but all distances are bounded by 1 in d'

Can somebody post challenging probability problems?

What's the probability that all non-trivial zeros of the Riemann zeta function have real part 1/2?

...

i also have the solutions, have fun user

1/2
1/2
1/2
either it is or it isnt
probability is easy

Can someone calculate the probability than any of these answers is within some margin of error?

Hello, i have a linear algebra question. Can someone help me understand the relationship between the trace of an n x n matrix A, and the eigenvalues of matrix A

sum of eigenvalues is equal to the trace of the matrix

Ok I see, what about the eigenvectors for A

There is a 100% chance you are pissing me off

what about them?

When they say "vanishes" do they mean goes to 0 or becomes discontinuous?

well I would to find the eigenvalues of A using only the determinant and trace.

(not the same guy)
Can you recall the definition of eigenvalue and eigenvector off the top of your head?

zero
that theorem is called L'Hospital's rule

idk. i know the determinant is 0

>he fell for the category theory meme

You Always should read the theory from you textbook before trying to do excercises/examples.
An eigenvector v is a (non zero) vector which A only scales by a factor of λ (it can't rotate it or do something else). λ is called the eigenvalue corresponding to v. In more compact notation Av=λv, or you can also write it this way (A-λI)v=0.

If A had an eigenvalue λ, then you would have (A-λI)v=0 for some non-zero v.
This happens if and only if A-λv is non invertible.
Which happens if and only if the determinant of A-λv is 0.

Thus λ is an eigenvalue if and only if det(A-λv)=0.
Therefore, you can find all the eigenvalues from this equation.

Now, say you solved the system and you found the eigenvalues. Take one of the eigenvalues, let's say λ.
The eigenvectors v corresponding to λ must, by definition, satisfy the following:
Av=λv, or in other words (A-λΙ)v=0. That's a linear system that you have to solve. The solutions are the eigenvectors for λ.

Watch this:
youtube.com/watch?v=PFDu9oVAE-g

I just need to figure out how to find the eigenvalues of a 3x3 matrix given using the determinant and trace. But i understand eigenvalues and eigenvectors now

The determinant is the product of the eigenvalues and the trace is the sum of the eigenvalues.
You probably have more info about the matrix (e.g. you already know on eigevalue) which will allow you to just solve for the eigenvalues.

>>he fell for the category theory meme
I'm not a "he".

What are some hidden properties of finite abelian groups?

Stuck on a proof

Ignore this baitfag. There are many men and women who research category theory. Here is Eugenia Cheng, she does higher dimensional category theory and makes retard-proof youtube videos explaining basic category theory concepts.
youtube.com/watch?v=g47V6qxKQNU

I do pure category theory. It's super useful and interesting. Algebra nerds constantly misuse algebra terminology and notation while claiming that Algebra can be approached through category theory. I thought I'd give it a try and I'm finding it's actually quite hard. I suspect that the solution here may require some overly complicated (and somewhat contrived) approach where I construct something in the category of groups capturing the notion of conjugation and then send it out to the category of sets.

>misuse category theory terminology and notation
fixed

How do I prove something that's too obivous but still written as a standalone question

Write the statement formally (i.e. via it's formal definition) and derive it explicitly.

If a statement is too obvious to the point you can't write a proof about it then you either don't understand it and you fooled yourself, or you don't understand some new machinery that is used to prove the statement.

trying to understand Knuths abstraction of the Josephus Problem.

so pure mental masturbation basically

>meme

I know "natural" is a big one, but what are some more?

any takers?

I'm supposed to graph this to see the set of feasible solutions, and then use the slopes, but how am I supposed to graph this when the constraints are variables? Did I set this up incorrectly?

x_1 - # cakes sold
x_2 - # Pastries sold
b_1 - lbs of flour avail.
b_2 - lbs of sugar avail.

max 40x_1 + 9x_2
subject to
10x_1 + 3x_2

Is calc 2 harder than 1 and 3 or am i just retarded? i breezed through calc 1 but in calc 2 every exam takes more time then i have to complete it (ie im too fucking slow despite knowing the material) and i get a shitty grade. I think if i grind enough i can mange to get a B- overall.
should i just give up on taking any consecutive calc courses and change to a shitty non-engineer major?
should i give up on my dreams?

>shitty non-engineer major
Is there anything even shittier?

>is there anything even shittier?
not sure if you're saying that engineering is shitty or everything else is, but thanks for reading my entire post and replying with a dumb joke and completley ignoring my question

>completley ignoring my question
I didn't. I'm implying that engineering is mainly for retards so you shouldn't be too worried.

>I'm implying that engineering is mainly for retards so you shouldn't be too worried
if you havent taken calculus and your reply says nothing about calculus then obviously your post was neither an answer to my question or a meaningfull statement

>your post was neither an answer to my question or a meaningfull statement
It's actually both, think about if for a while and you should realize.

so i have suffered defeat at the hands of a N.E.E.T. larping as someone who has left his parents house and gotten an education thus interacting with people like a normal human would, but for some reason can only contribute via insult rather than any explaination of any kind or length.
why are you on Veeky Forums? do you visit the advice board and tell people their retarded while you wait on mommy to bring you tendies? please stop wasting air and join the military or something before you turn 30

You seem hostile. Are you hostile?

I didn't insult you though, I was simply stating a basic fact about you and most engineers. You didn't seem to realize it so I decided to help.
>why are you on Veeky Forums?
I'm not on Veeky Forums, I'm on /mg/. I couldn't care less about this board as a whole.
Not at all.

>simply stating a basic fact
Nah, you're misusing a meme term as an excuse for excess hostility. Nobody who comes to Veeky Forums uses that meme that way. Someone should probably ban you for being cancer at some point.

What are you even trying to explain? It seems like you have difficulty communicating.

>meme
see

I think you mispelled that there name friend

this is shit

o with a hat in French means that there was an s after it, but it stopped being pronounced after time passed.

>this is shit
What do you mean?

The first one isn't wrong, it's just incomplete. The second one is just

[math](I \wedge S) \leftrightarrow B[/math] which is equivalent to the conjunction of [math](I \wedge S) \rightarrow B[/math] and [math]B \rightarrow (I \wedge S)[/math].

goto the website its the fucking tits

this website is fucking awesome

lmfdb.org/EllipticCurve/Q/150/c/1

its everything i've been dreaming about once i started learning algebra, full classification, tables of properties

Soooo...Stewart or Spivak?

I would like to take a full semester course in every word in that diagram. Too bad my only option for getting the money to pay for it would have made it impossible to attend the classes.

>I would like to take a full semester course in every word in that diagram. Too bad my only option for getting the money to pay for it would have made it impossible to attend the classes.
Just read some books m8

Neither, since the subject is trash.