Mathematicians are not agreed on this point. Some use N and N+ to distinguish between the set of Natural numbers including 0, and not including 0.
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The set of natural numbers plus zero is the set of all non-negative integers. Please note that the definition for the set of natural numbers is ambiguous. Some definitions include zero, while others exclude it.
Yes.
The extended set of natural numbers, or the non-negative integers.
Integers
Whole numbers and natural numbers are the exact same, except that whole numbers include zero