Irrationality measure
In mathematics, an irrationality measure of a real number x {\displaystyle x} is a measure of how "closely" it can be approximated by rationals. If a function f ( t , λ ) {\displaystyle f(t,\lambda )} , defined for t , λ > 0 {\displaystyle t,\lambda >0} , takes positive real values and is strictly decreasing in both variables, consider the following inequality: 0 < | x − p q | < f ( q , λ ) {\displaystyle 0<\left|x-{\frac {p}{q}}\right|<f(q,\lambda )} for a given real number x ∈ R {\displaystyle x\in \mathbb {R} } and rational numbers p q {\displaystyle {\frac {p}{q}}} with p ∈ Z , q ∈ Z + {\displaystyle p\in \mathbb {Z} ,q\in \mathbb {Z} ^{+}} .