Translation and analysis of words by ChatGPT artificial intelligence
On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:
- how the word is used
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- it is used more often in oral or written speech
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- usage examples (several phrases with translation)
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What (who) is countably many - definition
![The [[Cantor pairing function]] assigns one natural number to each pair of natural numbers](https://commons.wikimedia.org/wiki/Special:FilePath/Pairing natural.svg?width=200 "The [[Cantor pairing function]] assigns one natural number to each pair of natural numbers")
Wikipedia
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
In more technical terms, assuming the axiom of countable choice, a set is countable if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said countably infinite.
The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers.
