/sci/ - Science & Math

https://www.youtube.com/channel/UCs4aHmggTfFrpkPcWSaBN9g/videos

Jewish infinity

>>9988088
Uncountability is literally a fucking spook.
We should only study computable analysis. So called 'real' analysis is a waste of time.

>>9988602
This. I always wondered what's wrong with just sticking to the rationals. After all, if the rationals are dense in the reals, can't they approximate any real number to arbitrary precision? That's what happens in practice anyways right?

>>9988605
Irrational numbers are inherently intresting. If you disagree, you're free to work in a rational only system, you just won't be closed under exponation, which will cause a bunch problems that you can work around. It'll be fun I think!

Math doesn't really have rules, if you don't find something fun or intresting, yoiree free to exclude it as long as you're clear.

>>9988605
Hello wildberger

>>9988605

Nope they can't. Irrational numbers could however^^ Your argument sounds like "Why study relativity when Newtonian Physics is close enough?"

>>9988605
Sure you could do that, but eventually you will want to say something like "nothing squares to 2, but I can take a sequence of rational numbers which get closer to each other, and whose squares approach 2". You'll have a bunch of similar results, where you need this awkward language just to state things like the intermediate value theorem, extreme value theorem, etc. Eventually you'll want to just consider the set of all such sequences of rational numbers, and give them a nice name to make your theorems less ugly. You'll say two sequences are equivalent if their difference tends to 0, you'll add, subtract, multiply, term by term, etc. Oops! You just constructed R.

>>9988947
>Nope they can't.
Wrong. Q is dense in R. This is like the first week of any intro to analysis class. Please only make condescending posts if you know what you're talking about.

>>9988958
Same clild be said to you friend. It should be obvious to anyone that math without irrationals is very different than math with irrationals. Many would say "wrong".

>>9988958

I never said you can't approximate numbers( you can't with functions by the way, e.g. thomaes function), it's just not what happens in practice. And if we start with "well approximations are good enough", why not just approximate pi with 4? That's not how mathematics works.

>>9988605
Quick, what's the length of the diagonal of a unit square?

>>9988605
>I always wondered what's wrong with just sticking to the rationals.
Brainlet detected. Math isn't about "sticking to X". It's about asking "what if Y".

>>9988088

>The statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms.
this is your brain on AC

>>9988539
I remember my mathematical groups teacher telling me about this Jewish symbol and how they wanted to obscure obvious shit, based.

>>9989348
Kronecker, go.

>>9988602
>the red lines don't intersect

>>9989684
The lines intersect at (1, 1)

>>9988088
dude bigger infinities lmao

ℵ

>>9991038
Nice try but the red lines are not defined at (1,1). That would be problematic.

how do you calculate limits without infinity? without limits you couldn't construct manifolds or spaces that they sit in. you couldn't talk about the dirac delta function, which is crucial for quantum mechanics.

>>9991637
>how do you calculate limits without infinity
This triggers me.
[math] \lim_{x \to \infty} f(x) = L \quad iff \quad \forall \epsilon > 0 \exists r>0 \forall x \geq r |f(x) - L| < \epsilon [/math]. Where the fuck does infinity figure there?!

>>9989199
That doesn't depend on AC you fucking brainlet.

>>9991704
>Where the fuck does infinity figure there?!
Right after the [math]x \rightarrow [/math] in your equation.

>>9989679
Kroniggah mah niggah