This set of numbers is called "Whole Numbers".
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Whole numbers are the set of natural or counting numbers inclding zero
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The answer depends on what is meant by "their opposites". If you mean additive opposites then the set is of all non-zero integers.
The set of Counting Numbers or Natural Numbersincludes positive integers but not negative integers or zero.The set is 1,2,3,4,5,6....and so on.
No.The natural numbers (ℕ) are defined in 2 ways:the counting numbers {1, 2, 3, ...};The counting numbers and zero, ie {0, 1, 2, 3, ...}Some definitions include zero, others do not. Either way, negative numbers are NOT included. The set of Integers (ℤ) is the counting numbers, their negatives and zero, ie {..., -3, -2, -1, 0, 1, 2, 3, ...}