cardinal number
Học thuậtThân thiện
Definition
Noun: A cardinal number is a number that expresses quantity, answering the question "how many?" It is used for counting and denotes the size or magnitude of a set, without indicating position or order.
Usage
Cardinal numbers are the fundamental numbers used for counting objects (e.g., one, two, three, four, five). They are distinct from ordinal numbers (e.g., first, second, third), which indicate position or sequence.
Examples
- The cardinal number "five" tells you the quantity of apples in a basket.
- In the set {A, B, C}, the cardinal number is three.
- "One hundred" and "one thousand" are examples of large cardinal numbers.
Advanced Usage
- In set theory, the cardinal number (or cardinality) of a set is a measure of the number of elements of the set. For infinite sets, different sizes of infinity are described by different cardinal numbers (e.g., aleph-null for the set of natural numbers).
- The concept is used in linguistics to distinguish between cardinal numerals (e.g., books) and ordinal numerals (e.g., the book).
Variants and Related Words
- Cardinal numeral: Often used synonymously in linguistics to refer to the word or phrase representing a cardinal number (e.g., "seven" is a cardinal numeral).
- Cardinality (noun): The mathematical property that a cardinal number represents; the size of a set.
Synonyms
- Counting number
- Natural number (in some contexts, though natural numbers typically start from 1, while cardinal numbers include 0)
Antonyms
- Ordinal number: A number indicating position in a sequence (e.g., first, second, third).
Noun
- the number of elements in a mathematical set; denotes a quantity but not the order