The Limits of Computation and Infinity

Math proves that some infinities are literally bigger than others. It is a concept

called diagonalization and it completely breaks your brain. Imagine trying to list every decimal

number. Cantor proved you can always invent a new number that isn't on your list

just by changing the digits down the diagonal. You can never list them all.

Here is why that is scary for tech. Every computer program is just code, which is countable.

But the amount of problems to solve is uncountable. That means there are infinitely more

problems than there are programs to solve them. Computers will literally never be able to

do everything.