algebraic number: meaning, definition, pronunciation and examples
Low (Specialized)Formal academic/technical
Quick answer
What does “algebraic number” mean?
A number that is a root of a non-zero polynomial equation with rational coefficients.
Audio
Pronunciation
Definition
Meaning and Definition
A number that is a root of a non-zero polynomial equation with rational coefficients.
A real or complex number that can be expressed as a solution to a polynomial equation with integer coefficients; numbers that are not transcendental numbers.
Dialectal Variation
British vs American Usage
Differences
No significant differences in definition or usage. Minor variation in teaching curricula emphasis.
Connotations
Highly specialized mathematical term with identical technical meaning and neutral connotation in both varieties.
Frequency
Equally low-frequency in both UK and US English, confined to advanced mathematics contexts.
Grammar
How to Use “algebraic number” in a Sentence
N (that) is an algebraic numberThe algebraic number satisfies the equation...X and Y are algebraic numbersVocabulary
Collocations
Examples
Examples of “algebraic number” in a Sentence
adjective
British English
- The algebraic number field is central to the proof.
- We studied algebraic number properties.
American English
- The algebraic number field is key to the proof.
- We examined algebraic number properties.
Usage
Meaning in Context
Business
Never used.
Academic
Exclusively used in advanced mathematics, particularly number theory, abstract algebra, and cryptography.
Everyday
Virtually never used.
Technical
Core term in pure mathematics, computer algebra systems, and theoretical computer science.
Vocabulary
Synonyms of “algebraic number”
Neutral
Weak
Vocabulary
Antonyms of “algebraic number”
Watch out
Common Mistakes When Using “algebraic number”
- Confusing it with an 'algebraic expression'. An algebraic number is a specific value, not an expression.
- Assuming all irrational numbers are algebraic; many (like π) are not.
- Using it as a countable noun incorrectly (e.g., 'He calculated three algebraics').
FAQ
Frequently Asked Questions
Yes. Any rational number a/b is a root of the linear polynomial bx - a = 0.
No. Algebraic numbers include complex numbers, like i (the imaginary unit), which is a root of x² + 1 = 0.
They are fundamental in pure mathematics (number theory, Galois theory). Applications exist in cryptography and error-correcting codes.
Yes. For √2, we can write x = √2, so x² = 2. This gives the polynomial equation x² - 2 = 0 with integer coefficients. Therefore, √2 is algebraic.
Algebraic number is usually formal academic/technical in register.
Algebraic number: in British English it is pronounced /ˌæl.dʒɪˌbreɪ.ɪk ˈnʌm.bər/, and in American English it is pronounced /ˌæl.dʒəˌbreɪ.ɪk ˈnʌm.bɚ/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
ALGEBRAIC NUMBER: ALways Gives Exact Roots, Being Real Answers In Equations, Clearly Not Unguessable, Made Exact, Rational.
Conceptual Metaphor
A number that obeys the 'rules' of algebra (polynomial equations).
Practice
Quiz
Which of the following is NOT an algebraic number?