The extended set of natural numbers, or the non-negative integers.
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Natural Numbers do not inculde 0
Yes, because natural numbers are your counting numbers (1,2,3,4...) Whole numbers are natural numbers and zero (0,1,2,3...) and integers are all of the natural numbers and their opposites and zero (...-3,-2,-1,0,1,2,3...).
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.
Negative integers are whole numbers but not natural numbers. Mathematicians are undecided about zero. It is a whole number: some believe zero is a natural number, others do not.
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.