Question

4. Let Z be the set of all integers (positive, negative and zero.) Write a

sequence containing every element of Z.

Answer 1

Let Z be the set of all integers (positive, negative and zero.)

All whole numbers, positive, negative and zero form the set of integers. It is denoted by Z. So a sequence containing every element of Z = {-n,..., -3, -2, -1, 0, 1, 2, 3, ...n}

the set Z of all integers (positive, negative and zero) and the set Q of rational numbers are equinumerous with N. That is surprising, since N is a strict subset of Z and can be easily visualized to be embedded inside Q.

Since Z is equinumerous with N, we can also count or enumerate the elements of Z, so that for every n ? N we can identify an integer an as the n-th integer. For example, Z = {-n,..., -3, -2, -1, 0, 1, 2, 3, ...n}