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.
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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
Get a proper subset of whole numbers.
If N is the set of natural numbers, and the set of whole numbers (integers) is Z, you should be aware that Z also includes negatives and zero, whereas N does not include either of these.