Neither the sets of negative and positive integers (-1,-2,-3-,4... or 1,2,3,4...) contain zero (0). The set of natural numbers (... -4,-3,-2,-1,0,1,23,4...) does
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No.
You can think of lots of sets that don't contain a number; or that contain it for that matter. In this case, the most natural such set is probably the set of natural numbers, {0, 1, 2, 3, ...}. Another example would be the set of even numbers: {0, 2, -2, 4, -4, 6, -6, ...}.
You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).
The set of whole numbers.
I am assuming the you do not mean "group", which has a very specific mathematical meaning, but "set". The numbers belong to any set that will contain them! For example, {0, 3, 6, 27, 80}; {0, 3, pi, 6, sqrt(105), 27, 80}; N, the set of natural numbers, Z, the set of integers, Q, the set of rational numbers, R, the set of real numbers, C, the set of complex numbers, the set of integers between -30 and +130, the set of rational numbers between -97/4 and 641/5, the set of positive square roots of all non-negative numbers less than 9000.