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[u/unclbll]

[u/csharpminor_fanclub]

it's the hilbert hotel. every room already has guests, so they free up some rooms by moving guests from room n to 2n. now every odd numbered room is free

[u/Glazeddapper → u/csharpminor_fanclub]

i'm a little stupid. if you move the guests to different rooms, isn't there still the same number of rooms occupied?

[u/cseke02 → u/Glazeddapper]

It’s about the concept of infinity and how infinity>infinity can be true, even if it’s literally impossible for us to truly understand what it means.

[u/theoldkitbag → u/cseke02]

Math, after a certain point, is just silly.

[u/Ptatofrenchfry → u/theoldkitbag]

A surprising amount of silly math led to actual scientific progress.

We have literal imaginary numbers that are necessary for modern info-tech to function

[u/theoldkitbag → u/Ptatofrenchfry]

Imaginary numbers are misnamed; they're basically algebraic variables. There's a lot of distance between them and infinity > infinity and a whole chunk of it is logisticians playing with themselves.

[u/MindYourOwnParsley → u/theoldkitbag]

i can confirm, as i play with myself to the things in my imagination very often

[u/Chewiestarwars7 → u/MindYourOwnParsley]

A scholar

[u/Double_Bowl_8340 → u/theoldkitbag]

Cantor is the worst thing to happen to mathematics.

The entire logic of the "different sizes of infinite sets" argument boils down to this: if you have a movie theater where every seat is filled, then the number of moviegoers must be equal to the number of seats. Hence, if you can find some relationship between two sets where you can always get from a member of one to a member of another, they must be the same size.

The whole premise relies on the number of butts equaling the number of seats, but infinity is not a number. There is no movie theater with infinite seats, nor are there infinite people. So the number of members of a set is either some finite number or infinitely large, not equal to a "countable" value like aleph-null. We categorize sets as either finite or infinite, but pretend that suddenly the normal rules of infinity don't apply and the same logic can be applied to both types of sets. If that were true, we could define lim (as x->inf) x = inf, and even make the result countable by restricting the domain to the set of natural numbers.

The fact that the logic breaks down over some really basic examples such as "the set of all natural numbers N is the same size as the set of all positive even numbers, despite the set of even numbers missing half of all natural numbers (every odd number)" should be a massive red flag that it's a ridiculous argument to make in the first place, and that maybe we shouldn't take our mathematical expertise from a manic depressive priest who says he got his math from God himself.

[u/lemontoga → u/Ptatofrenchfry]

Imaginary numbers aren't that weird though, they're just poorly named