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natural numbers
These comprise the set of integers. Incidentally, 0 is a natural number.
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...).
It is the set of integers, denoted by Z.
They are called rational numbers. The set of rational numbers contains the opposites of its members.