transcendence
n.n. the quality of being so great or perfect that it goes beyond normal limits. In math, it describes a number or function that cannot be expressed as a simple fraction or a finite decimal.
n. the quality of being beyond ordinary limits or the state of surpassing a particular level. In a mathematical context, it refers to the property of a number or function that cannot be expressed as a ratio of two integers or a finite series.
The beauty of the painting reached a level of transcendence.
Mathematicians often study transcendence to understand which numbers, like pi, cannot be the solution to a polynomial equation with integer coefficients.
The concept of transcendence in mathematics highlights the distinction between algebraic numbers, which are roots of polynomials, and those that remain forever beyond the reach of such definitions.
From transcend + -ence.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.
Last updated May 19, 2026