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algebraic number

algebraic number noun: a complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.

Noun

algebraic number (plural algebraic numbers)

  1. A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.
    • The golden ratio (φ) is an algebraic number since it is a solution of the quadratic equation x²-x-1=0, whose coefficients are integers.
    • The square root of a rational number, √, is an algebraic number since it is a solution of the quadratic equation nx²-m=0, whose coefficients are integers.

algebraic number meaning in Tamil and Thai

algebraic number in Tamil

இயற்கணித எண்

algebraic number in Thai

element of a number field that is a root of a polynomial with integer coefficients
จำนวนเชิงพีชคณิต jam-nuuan-chəəng-pii-chá-ká-nít

Examples of algebraic number in a sentence

  • Thus, the equation x-eʸ#61;0 is satisfied for x#61;1,#92;y#61;0 and for no other pair of algebraic numbers.1918, The American Mathematical Monthly, volume 25, Mathematical Association of America, page 435:
  • As a matter of fact, it is not true that the algebraic numbers above can be factored uniquely, but the first case of failure occurs when p = 23.1921, L. J. Mordell, Three Lectures on Fermat's Last Theorem, page 16:
  • (i) It is easily checked that the set of all algebraic numbers is countable, whereas the set of all complex numbers is uncountable (this non-constructive proof goes back to Cantor).1991, P. M. Cohn, Algebraic Numbers and Algebraic Functions, Chapman & Hall, page 83, The existence of such 'transcendental' numbers is...

Forms of algebraic number

pluralalgebraic numbers

Words formed from algebraic number

Questions about algebraic number

What does algebraic number mean?
Algebraic number means a complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.
What is algebraic number in Tamil?
Algebraic number in Tamil is இயற்கணித எண். See Algebraic number meaning in Tamil.
How do you use algebraic number in a sentence?
Thus, the equation x-eʸ#61;0 is satisfied for x#61;1,#92;y#61;0 and for no other pair of algebraic numbers.
What part of speech is algebraic number?
Algebraic number is a noun.
What is the plural of algebraic number?
The plural of algebraic number is algebraic numbers.

Words near algebraic number in the dictionary

  1. algebraic integers
  2. algebraic K-theory
  3. algebraic normal form
  4. algebraic notation
  5. algebraic notations
  6. algebraic number
  7. algebraic number field
  8. algebraic number fields
  9. algebraic number theory
  10. algebraic numbers
  11. algebraic poset

Source and license

Adapted from Wiktionary: algebraic number (page history and authors); algebraic number (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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