Transcendental Number (Noun)
Meaning
An irrational number that is not algebraic.
Classification
Nouns denoting quantities and units of measure.
Examples
- The discovery of transcendental numbers revealed a new class of irrational numbers that could not be expressed as the root of a polynomial equation with rational coefficients.
- Pi is a well-known example of a transcendental number, and its unique properties have been extensively studied in mathematics.
- In 1882, Ferdinand von Lindemann proved that the number e is a transcendental number, providing a significant breakthrough in the field of mathematics.
- One of the fundamental theorems in mathematics states that almost all real numbers are transcendental numbers, including many mathematical constants.
- The distinction between algebraic and transcendental numbers has far-reaching implications for various mathematical theories and applications.