transcendental number (Meaning)
Wordnet
transcendental number (n)
an irrational number that is not algebraic
Synonyms & Antonyms of transcendental number
No Synonyms and anytonyms found
transcendental number Sentence Examples
- Transcendental numbers, which cannot be expressed as roots of polynomial equations with rational coefficients, fascinate mathematicians with their enigmatic properties.
- The number e, the base of the natural logarithm, is a well-known example of a transcendental number.
- Transcendental numbers play a significant role in number theory, including their applications in areas like Diophantine approximation and prime number theory.
- The classification of transcendental numbers remains an active area of research in mathematics, with constant breakthroughs and conjectures.
- The Gelfond–Shnirelman theorem provides a powerful tool for establishing the transcendence of certain numbers.
- The Lindemann–Weierstrass theorem proved that the number π is transcendental, paving the way for new advancements in transcendental number theory.
- Transcendental numbers have applications in complex analysis, where they are used to study the properties of entire functions.
- The set of transcendental numbers is uncountable, implying that there are infinitely many such numbers.
- The study of transcendental numbers has deep connections to areas such as algebra, geometry, and physics.
- Transcendental numbers continue to captivate researchers and mathematicians alike, inspiring discoveries and shaping our understanding of the mathematical landscape.
FAQs About the word transcendental number
an irrational number that is not algebraic
No synonyms found.
No antonyms found.
Transcendental numbers, which cannot be expressed as roots of polynomial equations with rational coefficients, fascinate mathematicians with their enigmatic properties.
The number e, the base of the natural logarithm, is a well-known example of a transcendental number.
Transcendental numbers play a significant role in number theory, including their applications in areas like Diophantine approximation and prime number theory.
The classification of transcendental numbers remains an active area of research in mathematics, with constant breakthroughs and conjectures.
