Mathematics

@nbro I happened to notice you didn't say anything whatsoever about who was considering that minimization or any context about it.

nbro

1:27 AM

@Simple I know what's minimization or maximization of a function

my problem is related to that specific function

@arctictern the context is non-linear square problems

Simple

the $1/2$ just for convenient when you differential the $\Vert\cdot\Vert^2_2$

nbro

@Simple well, but that still doesn't make much sense because you can simply omit the square and the 1/2

Adeek

1:52 AM

@arctictern are you familiar with triangulated categories ?

@nbro I take it you're trying to minimize $\|f\|$? If so, it's easier to minimize $\|f\|^2$, and the $\frac{1}{2}$ factor makes everything physicsy (energy is $\frac{1}{2}mv^2$, the antiderivative of $x$ is $\frac{1}{2}x^2$, etc.). Saying that making a problem easier "doesn't make much sense" is rather weird. Do you think it "doesn't make much sense" to have a remote when you can "simply" get up and click buttons on the TV?

lol

Yeah, so the point here is $\|f\|^2$ is easier to minimize than $\|f\|$. Think about the standard norm in $\Bbb R^n$, man.

You just kick the square root out from the definition.

Simple

lol

At first I was wondering how a seemingly innocuous question got 10 net downvotes! And then saw the comments haha

18 hours ago, by GPhys

check comments hahahaha http://math.stackexchange.com/questions/2212731/airthmatic-progression

op might be a troll making fun of OPs that come to MSE to get people to do their work for them.

april 1st and all

2:03 AM

Hi all. Hi @Balarka @arctictern

hello

@arctictern Riiight. Maybe

Hi @Brody!

Makes a ton of sense tbh. Good trollzing

Hey, how's it going @Balarka? :)

probably my favorite april fool joke: i.stack.imgur.com/4o7F8.jpg

Well, no, it's horrible but the comic was a good read.

2:09 AM

That's good humor

Funny art style though

Right? I really like that comic

Adeek

@arctictern I want to see if my understanding of exact triangles is correct.

share.pho.to/Af28Y

I think the usual batman community laughed at the idea when Grant Morrison told them what he's doing

Adeek

There is a class of exact triangles means there is some object in this specific category

which satisfies some construction ? or is it something different ?

@BalarkaSen Not too familiar with the subject tbh

2:13 AM

@Brody It's just comic stuff :P

Question... Does non-rational number mean anything contrary to irrational? Encountered a poster who used this term

how's things going?

Not bad. Mental-emotional wellness is improving-ish and I'm sensing a renewal for interest in mathematics

Learned some kinda fun stuff recently in real analysis. Open, closed sets. Isolated, limited points

Nice

How about you?

Oh, nevermind about the non-rational thing. It was clearly just for emphasis

2:22 AM

I'm alright. Still learning math, and doing stuff

So, can you give an example of subset of $\Bbb R$ which is infinite and every point is isolated? (PS: This is easy)

$\Bbb Z$

Can you make that uncountable?

@BalarkaSen Good to hear. What's your current study btw?

Mmm one sec

Set of harmonic numbers

Oh wait

Uncountable

Right.

@Brody some objects called "foliations"

I'm blanking atm. Is this trivial?

2:27 AM

Nah.

Hmm

Is it a famous construction?

vOv. Note that the answer to my question can both be yes or no.

Here's another question. Can you even give an uncountable subset such it is dense nowhere? That is, for any $p \in X$ and for any interval $[p-\epsilon, p+\epsilon]$ around it the set of limit points of $X \cap [p - \epsilon, p + \epsilon]$ is no more than $X$?

Rationals (albeit countable) are on the extreme end; dense everywhere.

It's tough for me

Keep it at the back of your head and chew on it occasionally :)

Of course, it can't be an interval or union of intervals intersect the rationals, irrationals, transcendentals

2:40 AM

mhm.

Well, forget the rationals especially lol. But segments of the continuum and alike things are the only uncountable subsets I can imagine atm, and these are all dense!

Yup.

Note that both questions are about how sparse uncountable sets can be. The first is stronger than the second; if it's isolated at every $p$, you can pick $\epsilon$ such that X cap [p-$\epsilon$, p+$\epsilon$] is just p.

So if you can answer the first affirmatively you have answered the second. The second can be true even if the first fails however

Of course, both can fail

Right

3:13 AM

So every member of $\Bbb Q$ is a limit point, and the set is everywhere dense. But no member is an interior point. This is weird stuff

Or at least certainly, the terminology is weird

Hello everyone

Hi

@Brody $\Bbb Q$ being dense in $\Bbb R$ means every real is a limit point of the rationals.

@BalarkaSen Thought so, but idk formally how they're related. I need to work on denseness

I've been thinking about the sum of the numbers 10 to 1, and have come to a few conclusions, I'm trying to find more information on it but my idea is very abstract. I've never heard anything about it and see no applications of it, but it's real and it has clear patterns.

3:16 AM

Yes, every member of $\Bbb Q$ is a limit point of itself (constant sequence $p, p, p, \cdots$ for any $p \in \Bbb Q$) - but that holds for any subset of R. Interior points of a subset $X$ are points a small neighborhood around which fits entirely in $X$

But any small neighborhood around any rational contains a lot of irrationls, so can never fit in $\Bbb Q$

This is basically it, I'll explain it here.

Imagine you're 5 feet from a wall, and you have to move 10 feet, 9 feet, 8 feet, 7 feet ....1 foot.

@Brody Formally how what are related?

and if you reach the wall you have to walk in the opposite direction the amount of feet left in the numbers.

@BalarkaSen Denseness and limit points. In reality, I know little of the latter and less of the former