In Reply to: Discussion question posted by Daniel Goroff on October 15, 1999 at 01:08:35:

Z_7 may be a smaller field, but it does not contain a copy of the positive integers. The elements of Z_7 are equivalence classes. These equivalence classes are subsets of Z which collectively contain all elements of Z+, but are not themselves integers. Since the elements of Z_7 are not integers, Z_7 does not contain a copy of Z+.

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>>Z_7 may be a smaller field, but it does not contain a copy of the positive integers.  The elements of Z_7 are equivalence classes. These equivalence classes are subsets of Z which collectively contain all elements of Z+, but are not themselves integers.  Since the elements of Z_7 are not integers, Z_7 does not contain a copy of Z+.