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 …

Apr 10, 2025 · But a computable function is a special case of an arbitrary function, so our enumeration is a computable enumeration of arbitrary functions, and the computable function we get at the end not …

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 …

Apr 5, 2023 · The reasoning I have seen goes is that Loader's Number is the largest computable number and TREE (3) and SSCG (3) are ostensibly computable numbers. But how do we know that: …

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 …

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 …

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.

Nov 13, 2024 · The Church Thesis asserts that every total function is computable. We can view a total function N → {0, 1} N → {0, 1} as a binary expansion of a number in [0, 1] [0, 1]. In this way, to every …

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 …

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 …