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There are very few that I can think of. The properties all depend on the domain and operations defined on the numbers in the domain.

Addition is commutative and transitive.

Multiplication is commutative and transitive.

Multiplication is distributive over addition.

I think that is it.

No property which has anything to do with the following operations can be a property for all numbers:

Subtaction: The set of positive numbers is not closed under subtraction.

Division: The set of all integers is not closed under division.

Indices: The set of rational numbers is not closed under indices (powers).

Ordering: The set of complex numbers is not (simply) ordered.

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Q: What property is for any numbers?
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