Height

The height of a rational number is defined to be the greater of the absolute values of its numerator and denominator in lowest terms.

If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gcd(m,n)=1} , then Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H\left(\frac m n\right) = \max(|m|,|n|)} .

Height is used in the method of infinite descent to prove that some property is true of all rational numbers, when it can be shown that the property is true of any rational number whenever it is true of all rational numbers of lesser height.