system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 What is aleph null? I’ve heard somewhere that it is the smallest infinity, but that doesn’t make sense.

Edit: Didn’t think it would be this complicated. My brain is overheating ._.
gpt
There are objects in mathematics that called sets which are literally sets of something. It may be people in the room, apples on tree, coins in your pocket, numbers, vectors and pretty much anything. The amount of things in set is cardinality. It's pretty simple if you count people in the room - the cardinality of such set will be equal to the amount of people. It's a bit more complicated when you speak about infinite amount of something.

Aleph null is the amount of all natural numbers. There is infinite amount of those but still we can count them: 1,2,3 etc. Some other sets have the same cardinality because there is a theorem and we can count the elements in such sets. Eg we can count all whole numbes: 0, 1, -1, 2, -2, 3, -3 etc. It's a bit funny that it seems you take twice as much numbers but their amount is the same.

But you can't count all real numbers: between two any real numbers you can put as many other real numbers as you want: you can pit 0.5 between 0 and 1, you can't put 0.25 between 0 and 0.5 etc, so it appears that the amount of real number is also infinite but this infinity is greater than aleph-null.