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

• 1, 2, 3, 4, $\ldots$
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
MathematicsTaxonomy Factorial
GeorgCantor
CompositeNumber
Eratosthenes
Euclid
EuclideanAlgorithm
FactoringIntegers
FermatNumber
FermatsLittleTheorem
Goldbach
ImproperFraction
MersennePrime
MultiplyingWholeNumbers
PrimePair
RationalNumber
RiemannHypothesis
RiemannZetaFunction
RootTwoIsIrrational
SieveOfEratosthenes
SquareNumber
SubtractingWholeNumbers
Surd
TranscendentalNumber
TransfiniteNumbers
ZornsLemma
NaturalNumber ContinuumHypothesis
CountableSet
MixedNumber
PerfectNumber
TypesOfNumber
UncountableSet
WholeNumber

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CountingNumber
Integer
WholeNumber (none) RealNumber