Math people changed their mind, but for historical reasons there is some confusion.¹
Natural numbers are defined by successively adding 1 and zero is the neutral element of addition.
It's much easier to operate on sets with neutral element included!
Most integer operations (at least in Perl) can return 0.
For instance otherwise adding the sum of the first index of two arrays would be 2 (the second element) instead of 0 (again the first)
( addicted to the Perl Programming Language)
1) the concept of natural numbers was older than group theory