Computable real function: Difference between revisions

Revision as of 04:23, 9 May 2015

Latest revision as of 20:47, 27 April 2020

Line 1:

In [[mathematical logic]], specifically [[recursion theory|computability theory]], a [[Rangefunction (mathematics)|function]] <math>f \colon \mathbb{R} \to \mathbb{R}</math> is ''sequentially computable'' if, for every [[computable sequence]] <math>\{x_i\}_{i=1}^\infty</math> of [[real number]]s, the [[sequence]] <math>\{f(x_i) \}_{i=1}^\infty</math> is also [[computable real number|computable]].

A function <math>f \colon \mathbb{R} \to \mathbb{R}</math> is ''effectively uniformly continuous'' if there exists a [[primitive recursive function|recursive function]] <math>d \colon \mathbb{N} \to \mathbb{N}</math> such that, if