real number
Low (technical).Technical/Scientific (Mathematics, Physics, Computing).
Definition
Meaning
Any rational or irrational number; any number that can be found on the number line, including all integers, fractions, and infinite decimals.
In non-mathematical contexts, sometimes used loosely to refer to a specific, definite number as opposed to an estimate or a hypothetical value (e.g., 'give me a real number').
Linguistics
Semantic Notes
Contrasts specifically with 'imaginary number' (involving √-1) and 'complex number' (a combination of real and imaginary parts). The term is absolute in mathematics, but its metaphorical use in everyday language is informal.
Dialectal Variation
British vs American Usage
Differences
No significant differences in the mathematical term. The informal metaphorical use ('a real number' for a concrete figure) is marginally more common in American business contexts.
Connotations
In academic contexts, identical and precise. In informal use, 'real number' can imply 'tangible, concrete figure' in both varieties.
Frequency
Equally low-frequency and specialized in both dialects. Understood primarily by those with secondary education in mathematics.
Vocabulary
Collocations
Grammar
Valency Patterns
[real number] + [verb: is, lies, represents][verb: define, represent, calculate] + [as a real number][preposition: on] + [the real number line]Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “[No common idioms based on this specific technical term]”
Usage
Context Usage
Business
Rare. Might appear in data analysis or financial modelling discussions: 'We need to input a real number here, not a percentage.'
Academic
Primary context. Used in mathematics, physics, engineering, and computer science courses and literature.
Everyday
Very rare. Possible informal metaphorical use: 'I asked for the cost, but he wouldn't give me a real number.'
Technical
Standard, precise term in mathematics, scientific computing, and engineering specifications.
Examples
By Part of Speech
verb
British English
- [No standard verb form derived from this noun phrase]
American English
- [No standard verb form derived from this noun phrase]
adverb
British English
- [No standard adverb form derived from this noun phrase]
American English
- [No standard adverb form derived from this noun phrase]
adjective
British English
- The variable must hold a real-number value.
- We are operating in a real-number domain.
American English
- Ensure the output is a real-number quantity.
- The function is defined for all real-number inputs.
Examples
By CEFR Level
- Five is a real number.
- Find some real numbers on this number line.
- Fractions like ½ are also real numbers.
- The square root of 4 is a real number.
- Not all equations have solutions that are real numbers.
- The set of real numbers includes both rational and irrational values.
- The continuity of the function depends on the density property of the real numbers.
- In complex analysis, every real number is a complex number with a zero imaginary part.
Learning
Memory Aids
Mnemonic
REAL numbers live on the REAL number line. If you can point to a spot on the continuous line, it's a real number.
Conceptual Metaphor
CONTINUITY IS A LINE (The real numbers are conceptualised as a continuous, unbroken line).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Direct translation 'настоящее число' is incorrect for the mathematical term. The correct translation is 'действительное число'.
- Avoid confusing with 'rational number' (рациональное число) or 'integer' (целое число).
Common Mistakes
- Using 'real number' to mean 'round number' or 'whole number'.
- Confusing 'real' (действительное) with 'actual' or 'true' in translation.
- Pronouncing 'real' as /ri:l/ (like 'reel') in British English; the standard is /rɪəl/.
Practice
Quiz
Which of the following is NOT a real number?
FAQ
Frequently Asked Questions
Yes, zero is a real number. It is an integer and lies on the number line.
Integers are whole numbers (e.g., -2, 0, 7). Real numbers include all integers PLUS all fractions and infinite decimals (e.g., 0.5, √2, π). All integers are real numbers, but not all real numbers are integers.
Yes. The square root of negative one (√-1), denoted as 'i', is an imaginary number and is not a real number. Complex numbers like 3 + 2i are also not purely real.
The term originated historically to distinguish these familiar numbers from the seemingly less tangible 'imaginary numbers', which were initially considered fictitious or useless abstractions.