I heard about it while watching a TV show, and even after reading through the wikipedia I cannot understand it. [Here](https://en.m.wikipedia.org/wiki/Cantor%27s_paradox) is the wiki for reference. I’d like to understand what the “paradox” behind this is because these sort of things bother me and I feel like I won’t be able to continue without understanding. Thanks in advance!
In: 2
How many numbers are there?
We could put them all in a box^1, and count how many things are in the box^2 . That’s how many numbers there are. Let’s call it C.
But what if we took a random selection of numbers from the box. How many possibilities are there^3 ? Well, for every number in the box, we either select it or we don’t. This means that we can calculate the number of possibilities by 2^C , as it’s C binary choices.
But hold on: 2^C > C
This means that either:
We have all the numbers at least up to 2^C , and there are more than C numbers
We have only some of the numbers up to 2^C , so our set of all the numbers is missing some.
Either of these options is a contradiction
_____
1. The box is a set.
2. This is the cardinality of the set.
3. The set of these possibilities is the powerset of the original set.
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