transcendental number Sentence Examples

1. Transcendental numbers, which cannot be expressed as roots of polynomial equations with rational coefficients, fascinate mathematicians with their enigmatic properties.
2. The number e, the base of the natural logarithm, is a well-known example of a transcendental number.
3. Transcendental numbers play a significant role in number theory, including their applications in areas like Diophantine approximation and prime number theory.
4. The classification of transcendental numbers remains an active area of research in mathematics, with constant breakthroughs and conjectures.
5. The Gelfond–Shnirelman theorem provides a powerful tool for establishing the transcendence of certain numbers.
6. The Lindemann–Weierstrass theorem proved that the number π is transcendental, paving the way for new advancements in transcendental number theory.
7. Transcendental numbers have applications in complex analysis, where they are used to study the properties of entire functions.
8. The set of transcendental numbers is uncountable, implying that there are infinitely many such numbers.
9. The study of transcendental numbers has deep connections to areas such as algebra, geometry, and physics.
10. Transcendental numbers continue to captivate researchers and mathematicians alike, inspiring discoveries and shaping our understanding of the mathematical landscape.

transcendental number Meaning

Wordnet

transcendental number (n)

an irrational number that is not algebraic

Synonyms & Antonyms of transcendental number

No Synonyms and anytonyms found

FAQs About the word transcendental number

What is the meaning of the word transcendental number

an irrational number that is not algebraic

What are the synonyms of the word transcendental number

No synonyms found.

What are the antonyms of the word transcendental number

No antonyms found.

What is the usage of word transcendental number

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.

How to use the word transcendental number in a sentence?

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.