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WordNet-Online
Definitions from WordNet | ||||
Definitions from the WebTerm: Transcendental NumberA transcendental number is a type of real number that is not a root of any non-zero polynomial equation with integer coefficients. In other words, it cannot be expressed as a fraction or a root of a natural number. Transcendental numbers are an important concept in mathematics and have unique properties. Examples:Sense 1: In mathematics, a transcendental number can be represented by π (pi). It is an irrational number that cannot be expressed as the ratio of two integers. For example, the circumference of a circle divided by its diameter is a transcendental number. Sample sentence: "The value of π is an example of a transcendental number, with its famous approximation of 3.14159 and its infinite decimal representation." Sense 2: Transcendental numbers also occur in other areas of mathematics such as complex analysis and number theory. They play a crucial role in the study of functions and equations. Sample sentence: "The existence of transcendental numbers was proven by Ferdinand von Lindemann in 1882, which had profound implications for mathematical theory." Sense 3: In a philosophical context, transcendental numbers can be seen as transcending rational and algebraic numbers, exhibiting a certain level of "unattainableness" or beyond ordinary understanding. Sample sentence: "In philosophy, transcendental numbers symbolize the realm of unknowable truths, beyond the reach of human comprehension." Related products on Amazon: | ||||
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