0, 1, 2, 3, 4, etc. are called Cardinal Numbers.
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The counting numbers are the whole numbers that start at 1 and end at infinity. Although zero is considered a whole number, it is not a counting number.
The set of whole numbers.
The sum of the first 50 counting numbers, excluding zero, is 1,251.
The counting numbers are {1, 2, 3, ...}. The integers are the counting numbers, their opposites (-1, -2, ...) and zero. So they are {..., -2, -1, 0, 1, 2, ...}.
Zero (0) is in the set of whole number. The only difference between the set of whole numbers and counting numbers is that the whole numbers contain zero. {0,1,2,3...}