A key point is that the representation functions and numbering functions are not themselves "computable" by the model of computation. The purpose of these functions is to translate other …

Sep 10, 2023 · Yes, all computable numbers are definable but not all definable numbers are computable. Informally, a computable number is one for which we can write a computer program …

Is this true, that if we can describe any (real) number somehow, then it is computable? For example, π π is computable although it is irrational, i.e. endless decimal fraction. It was just a luck, that there are …

Oct 28, 2020 · Computable real numbers are algebraically closed - every reasonable operation you do with them will result in another computable numbers. That is the essence of the statement.

Apr 9, 2022 · ''f is computable if there is a computable function f^". The general definition of computability refers to the function f^. This is what a computable function is. In your text, another …

Sep 16, 2024 · To be clear, the computable numbers are real numbers which can be calculated to arbitrary precision by a finite, terminating algorithm - or in other words, by a halting Turing machine.

Mar 4, 2021 · According to Wikipedia, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. I'm somewhat confused here. I …

Dec 1, 2018 · My thoughts: I don’t quite understand or appreciate the difference between “computably generated” vs “computable”. I was comparing the definition especially comparing the definition given …

Dec 2, 2021 · This answer makes it sound like every number is computable. This is incorrect - every natural number is computable, but uncomputable numbers are a thing. So even though there is an …

Oct 13, 2024 · Yes, in a sense this is a consequence of the fact that the real numbers are uncountable whereas there will only ever be countably many strings in any finite alphabet. However this has to be …