Irrationality measure
id:
irrationality-measure-206-2636664
title:
Irrationality measure
text:
An irrationality measure of a real number α is a measure of how "closely" it can be approximated by rationals. If a function f, defined for positive real numbers, strictly decreasing in both x and λ is given, consider the following inequality: 0 < | α − p q | < f for a given real number α ∈ R and rational numbers p q with p ∈ Z, q ∈ Z +. Define M as the set of all λ ∈ R + for which only finitely many p q exist, such that the inequality is satisfied. Then λ = inf M is called an irrationality meas
brand slug:
wiki
category slug:
encyclopedia
description:
Function that quantifies how near a given real number is to being rational.
original url:
https://en.wikipedia.org/wiki/Irrationality_measure
date created:
2006-07-14T22:09:40Z
date modified:
2024-09-10T15:37:28Z
main entity:
image:
fields total:
13
integrity:
14