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## Homework Statement

Let * and = be defined by a*b means a - b is an element of the integers and a = b means that a - b is an element of the rationals. Suppose there is a mapping P: (* equivalence classes over the real numbers) --> (= equivalence classes over the real numbers). show that this mapping is onto and well defined.

## Homework Equations

None.

## The Attempt at a Solution

I'm confused, wouldn't this mapping NOT be onto? I mean, if you take all the equivalence classes defined by * it couldn't cover all the equivalence classes covered by =, since = deals with rationals and * integers. Is this a misprint in the book or am I mistaken?