You can have counting number in multiplication and addition.
All integers are in multiplication, addition and subtraction.
All rational numbers are in all four.
Real numbers, complex numbers and other larger sets are consistent with the four operations.
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Subtraction and addition are not properties of numbers themselves: they are operators that can be defined on sets of numbers.
For the specific case of whole numbers, you can consider multiplication to be repeated addition; and division to be repeated subtraction (see how often you can subtract something).
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
They are addition, subtraction, division and multiplication
parentheses, exponents, multiplication, division, addition, and subtraction.