# transcendence

/tɹænˈsɛndəns/ (US) · /tɹænsˈɛndəns/ (UK) · CEFR C1 · Noun

Source: https://englishreference.com/word/transcendence
Updated: 2026-05-19

## Definition

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.

For teachers: 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.

## Examples

- 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.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.