natural number
Definition
- Noun:
- A positive integer: A "natural number" is any member of the set {1, 2, 3, ...}, which starts from 1 and continues by repeatedly adding 1. It is a fundamental concept in mathematics used for counting and ordering.
Usage Examples
- Noun:
- Seven is a natural number. (Seven belongs to the set {1, 2, 3, ...}.)
- The set of natural numbers is infinite. (The collection of numbers 1, 2, 3, ... has no end.)
- We use natural numbers to count discrete objects. (Numbers like 1, 2, and 3 are used for counting individual items.)
Advanced Usage
- In set theory: The set of natural numbers is often denoted by the symbol ℕ.
- The properties of ℕ are studied in number theory.
- Debate on inclusion of zero: In some mathematical contexts, the definition is extended to include 0, forming the set {0, 1, 2, 3, ...}. To avoid ambiguity, the terms "positive integers" (for {1, 2, 3, ...}) or "non-negative integers" (for {0, 1, 2, 3, ...}) are often used.
- In computer science, natural numbers sometimes include zero.
Variants and Related Words
- Integer (n): A whole number that can be positive, negative, or zero (e.g., ...-2, -1, 0, 1, 2...). All natural numbers are integers, but not all integers are natural numbers.
- Whole Number (n): Often used synonymously with "integer," but in some contexts, it refers specifically to non-negative integers (0, 1, 2, 3, ...).
- Counting Number (n): A synonym for "natural number," emphasizing its use in counting.
Synonyms
- Positive integer: Specifically refers to numbers greater than zero (1, 2, 3, ...).
- Counting number: Highlights the number's primary use for enumeration.
Related Phrases
- Set of natural numbers: The complete collection of all natural numbers.
- The set of natural numbers is closed under addition and multiplication.
- Successor function: The operation of adding 1 to a natural number to obtain the next natural number.
- The successor of the natural number 5 is 6.
Noun
-
the number 1 and any other number obtained by adding 1 to it repeatedly
