a real number

USAGE SUMMARY

The phrase "a real number" is correct and usable in written English.
It is typically used in mathematics to refer to any value that can represent a distance along a continuous line, including both rational and irrational numbers. Example: "In calculus, we often work with functions that take a real number as input."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

That's a real number.

Yale University

It's a real number.

The New York Times

"It was a real number," he said.

The New Yorker

"Here's a real number," Rubin says.

The New Yorker

It can be "default" or a real number.

Harvard University

A real number is the familiar sort from normal arithmetic.

The Economist

"It is a real number," Mr. Gilmore said.

The New York Times - Tech

where is a real number.

Advances in Difference Equations

Parameter is a real number.

EURASIP Journal on Image and Video Processing

Let q > 1 be a real number.

Journal of Inequalities and Applications

Let ρ be a real number.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "a real number" in mathematical or technical writing, ensure that the context clearly defines the variable or parameter the number represents.

Common error

Avoid using "a real number" when you specifically need to refer to integers or rational numbers. Real numbers encompass both, but if precision is required, use the more specific term.

Linguistic Context

The phrase "a real number" functions as a noun phrase, typically serving as a subject, object, or complement within a sentence. As seen in Ludwig's examples, it frequently appears in mathematical or scientific contexts to define or describe numerical quantities.

Expression frequency: Very common

Frequent in

Science

55%

Academia

25%

News & Media

10%

Less common in

Formal & Business

5%

Encyclopedias

3%

Wiki

2%

Ludwig's WRAP-UP

In summary, the phrase "a real number" is a noun phrase commonly used in mathematical and scientific contexts to denote a value that can be represented on a number line. Ludwig's analysis confirms its grammatical correctness and widespread usage. While technically precise, it's crucial to ensure that its usage aligns with the specific type of number being referenced, especially distinguishing it from integers or rational numbers when necessary. As shown by Ludwig, the phrase appears most frequently in scientific and academic publications, reflecting its formal and technical nature.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a pragmatic number

Implies a number that is useful or practical in a specific situation.

a realistic number

Suggests a number that is achievable or likely to occur.

a substantive number

Emphasizes that the number is significant or considerable.

a concrete number

Highlights that the number is definite and not abstract.

a effective number

Suggests that the number is powerful in the current context.

a certain number

Refers to a number with a known or fixed quantity.

a fundamental number

Indicates a number that is basic or essential.

a definite number

Implies a number that is clearly defined or determined.

a practical number

Highlights the number's applicability or usefulness in real-world scenarios.

a correct number

Suggests that the number is accurate and without error.

FAQs

How is "a real number" used in mathematics?

In mathematics, "a real number" refers to any number that can be plotted on a number line. This includes rational numbers, like fractions, and irrational numbers, like pi or the square root of 2.

What is the difference between "a real number" and an integer?

An integer is a whole number (positive, negative, or zero), while "a real number" includes all integers, as well as fractions, decimals, and irrational numbers. All integers are real numbers, but not all real numbers are integers.

Can I use "numerical value" instead of "a real number"?

Yes, in some contexts, "numerical value" can be a suitable substitute for "a real number", especially when the specific type of number is not important.

What are some examples of what is NOT "a real number"?

Numbers that are not real include imaginary numbers (like the square root of -1, denoted as 'i') and complex numbers, which combine a real and an imaginary part. These numbers exist outside the standard number line.