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You are talking about rationals and algebraic numbers, which are just a tiny subset of the real numbers. Your point about computable vs non-computable numbers i
by meuk 8y ago
You are talking about rationals and algebraic numbers, which are just a tiny subset of the real numbers. Your point about computable vs non-computable numbers is valid, but I think the author meant that you will never encounter a real number that is non-computable, since those are impossible to express in the first place. Real numbers can contain an infinite amount of information.
- btilly 8y agoActually there are non-computable numbers known that you can encounter. See https://en.wikipedia.org/wiki/Chaitin%27s_constant https://en.wikipedia.org/wiki/Chaitin%27s_constant.
- chriswarbo 8y agoYes, there's actually another distinction we can make: between incomputable numbers and indescribable numbers. The latter is very slippery, since it can lead to things like the Berry paradox https://en.wikipedia.org/wiki/Berry_paradox https://en.wikipedia.org/wiki/Berry_paradox For example, we would need some way to avoid expressions like "the smallest indescribable number", since that itself is a description ;)