@Deusovi Soooooooo we just ended our discussion on the concept of infinity yesterday and my brain hurts

We started off with Hilbert's hotel, which like, okay, cool, makes sense

I've seen a lot of videos on it

And then we start getting into the fact that

All integers are the same sizes as the natural numbers

And that, in fact, all RATIONAL NUMBERS are the same as the integers, because you can make like a 2-d list of something

And then he showed how the size of all real numbers is the same as the size of all possible numbers between 0 and 1

AND THEN he went onto show how the size of the uncountable infinity is 2^aleph_zero

And then called the uncountable infinity as aleph_1 because "hey, it doesn't matter whether it's aleph_1 or aleph_2 because math still works regardless"

And then started talking about aleph_aleph (zero) or infinity_sub infinity

And it's still the size of my thumb

Help

@Sciborg also chat.stackexchange.com/transcript/message/43415914#43415914

So yeah guess who had a breakdown in the middle of Calc BC

Not me for sure

INFINITY IS THE SIZE OF MY THUMB

Is infinity the size of infinizty?

@PrinceNorthLæraðr no idea what you mean by this

if you're working with cardinalities (which you're doing here), and by "infinity" you mean some particular infinite number (e.g. ℵ₀), then yes, "infinity is the size of infinity" by definition

but my formalized version of that statement is roughly as novel as as "the absolute value of 5 is 5"

There are many different types of infinities. More than the number of finite numbers, in fact.

Basically two infinities are the same if you can biject between them (one-to-one correspondence between two sets means they must be the same size).

When you're looking at the set of all numbers between 0 and 1, don't think of its "size" as like the distance from 0 to 1! That would be measure theory, and you're not measuring the set, just counting its elements. Think of it as a set of dots where every dot is a number between 0 and 1. You can see that the set is infinitely big, there's infinitely many numbers between 0 and 1.

It makes sense that that set has the same size as the set of all real numbers, because there's a bijection between one set and the other. Think of the tan and arctan functions: you've got a bijective increasing function which maps one-to-one between a finite interval (-pi/2 to pi/2, but that can easily be changed to (0,1) by a linear transformation) and the whole real line.

Whereas the set of integers, or the set of rational numbers, is not the same size. You can count those sets, even if your counting goes on forever, but you can't count the set of real numbers, because you'll always miss some. Counting is basically an informal way of describing "bijects with the natural numbers": one, two, three, four, ...

Anyway, hope I'm not intruding @PrinceNorthLæraðr. I saw your link in the Lair and followed it for maths chat.

@Deusovi Haha, yes. The comment was more facetious than serious, it was a spoof off of the "size of all real numbers is the size of all numbers between 0 and 1

@Randal'Thor No, I appreciate it!

Every time you want to be facetious, remember that the word facetious contains all five vowels in alphabetical order exactly once.

WAIT WOAH

That's cool

@Randal'Thor Also, 'borg and I were chatting about this - was I annoying when I was younger? :P

thinking face

Not that I recall.

Mm

Is it because I'm still annoying? :PP

Heh, I was going to say that as a joke :-P

I remember a fair few SE people who ... let's say, needed a lot of patience, as youngsters. Don't remember you being one of them though.

I'm also not sure how old you are TBH. I'm going to say probably towards the upper end of teendom?

(feel free to not answer, of course)

@Randal'Thor Yup. 17 :P

@PrinceNorthLæraðr ABSTEMIOUS too! (and adding -LY to either of those gives you Y as well!)

and nah, you were fine in my book too

@Deusovi Hehehehe

Also turning 18 in two months :3

congratulations!

November is a strange time for a tree to be born. Normally they're dying at that time.

Conclusion: despite his name, North is from the southern hemisphere.

@PrinceNorthLæraðr \o/

Soon you can be prosecuted as an adult in court!

And you can vote!

And get married, make a will, and get loans!

All sorts of terrifying possibilities :D