In Reply to: Re: Discussion question posted by Daniel Goroff on October 19, 1999 at 20:34:27:

The copy of Z+ that the rationals contain are the equivalence classes {[x,1] such that x is an element of Z+} We could define another equivalence relation on the union of Z+ and Q that could technically relate each positive integer with a unique rational number. 7, for example, would be equivalent to [7,1]. We can't do this in Z_7 because there are only 7 equivalence classes in Z_7 but there are inifintely many numbers in Z+.

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>>The copy of Z+ that the rationals contain are the equivalence classes {[x,1] such that x is an element of Z+}  We could define another equivalence relation on the union of Z+ and Q that could technically relate each positive integer with a unique rational number.  7, for example, would be equivalent to [7,1].  We can't do this in Z_7 because there are only 7 equivalence classes in Z_7 but there are inifintely many numbers in Z+.