natural numbers

USAGE SUMMARY

The phrase "natural numbers" is correct and usable in written English.
It is typically used in mathematics to refer to the set of positive integers starting from 1, often including 0 depending on the context. Example: "In number theory, natural numbers are fundamental as they form the basis for counting and ordering."

✓ Grammatically correct

Science

Encyclopedias

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The natural numbers N.

Encyclopedia Britannica

Week 6: Dedekind's theory of natural numbers.

University of California, Berkeley

Every natural number has a successor in the natural numbers.

Encyclopedia Britannica

As an illustration involving infinite sets, N may be taken to denote the set of natural numbers 0, 1, 2, … (some authors exclude 0 from the natural numbers).

Encyclopedia Britannica

I start with Cantor's transcendental proof by diagonalization of the non enumerability of the collection of functions from natural numbers to the natural numbers.

Physics of Life Reviews

The numbers thus obtained are called the counting numbers or natural numbers (1, 2, 3, …).

Britannica

Finally, in the 1630s, the area under y = xk was found for all natural numbers k.

Britannica

Its home is in the natural numbers : 1, 2, 3, 4,.

Cornell University

Natural numbers.

SEP

What, then, are the natural numbers?

SEP

for the natural numbers, where.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When discussing "natural numbers", clearly define whether you include zero, as conventions vary across different mathematical contexts.

Common error

Avoid assuming that "natural numbers" always include zero. Always clarify if zero is included to prevent misunderstanding, as some definitions exclude it.

Linguistic Context

The phrase "natural numbers" functions as a noun phrase, typically serving as the subject or object of a sentence when discussing mathematical concepts. Ludwig shows it frequently appears in scientific and academic contexts.

Expression frequency: Very common

Frequent in

Science

50%

Academia

25%

Encyclopedias

25%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the term "natural numbers" refers to the set of positive integers, sometimes including zero. As Ludwig AI points out, this phrase is grammatically sound and most commonly appears in scientific and academic texts. When using "natural numbers", remember to clarify whether zero is included to avoid ambiguity. Alternative phrases include "positive integers" or "counting numbers". Always consider the audience and context when discussing mathematical concepts, and use precise language to ensure clear communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

counting numbers

Emphasizes the use of these numbers for enumeration.

positive whole numbers

Combines 'positive' and 'whole' to specify the type of numbers.

non-negative integers

Explicitly includes zero in the set.

positive integers

Focuses specifically on the positive subset, excluding zero.

the set of positive integers

Formalizes the concept as a set in mathematical discourse.

whole numbers (excluding negatives)

Highlights the non-negative and integer characteristic.

non-negative counting numbers

Specifies the inclusion of zero while still referring to their use in counting.

elements of the set ℕ

Refers to members within the standard mathematical notation for natural numbers.

enumeration numbers

Highlights their primary function in counting and listing items.

the counting sequence

Emphasizes the sequential aspect and use in ordering elements.

FAQs

Are "natural numbers" and whole numbers the same thing?

While often used interchangeably, "natural numbers" can sometimes exclude zero, whereas whole numbers typically include it. Clarify the context to avoid ambiguity.

What symbols are commonly used to represent the set of "natural numbers"?

The set of "natural numbers" is commonly denoted by the symbol ℕ.

How are "natural numbers" used in mathematics?

"Natural numbers" are fundamental in various mathematical fields such as number theory, combinatorics, and analysis, serving as the basis for counting and discrete mathematics.

What is the difference between "natural numbers" and "integers"?

"Natural numbers" are positive whole numbers (sometimes including zero), while "integers" include all whole numbers, both positive and negative.