https://www.youtube.com/watch?v=jlnBo3APRlU https://www.youtube.com/watch?v=jlnBo3APRlU The gist of the argument is that addition + other operations on non-com

https://www.youtube.com/watch?v=jlnBo3APRlU https://www.youtube.com/watch?v=jlnBo3APRlU The gist of the argument is that addition + other operations on non-computable numbers (which the real numbers contain) require infinite algorithms or something similar (unlike addition on computable irrational numbers which may require infinite work, but the algorithms are finite). You can therefore get situations where, say, the tenths digit in a sum of non-computable numbers is not defined because of potentially infinite carries, and there's no way to determine if the sequence of carries terminates or not. He discusses the problem in the context of different representations of real numbers, including infinite decimals, cauchy sequences, and dedekind cuts etc. This is just the gist of it.