A "Counting Number" is one of the positive integers:

Some people include $0$ as a counting number, and some people don't. It's largely a matter of convention - there is no "right" and "wrong" over this. When you need to be precise then use the terms "positive integers" to exclude $0$ and "non-negative integers" to include $0.$

Counting numbers are also sometimes referred to as the "Natural Numbers," although that creates the implication that somehow the non-counting numbers are in some sense "unnatural" - an unfortunate connotation.

Related: Integers
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NaturalNumber ContinuumHypothesis
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CountingNumber
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Integer
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WholeNumber (none) RealNumber

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