What is the range of "x-y is a rational number"? Where x and y are set of real numbers.
is it -- (0,0), (1/2,-1/2), (1/3, 4/3)?
Now, if you are merely asking what is the size of the set (i.e. The set of all real numbers x and y such that x - y is rational) then your answer is that the size of your set is infinite. Given any value of x we can find an infinite number of y values such that x - y is rational.
I think this addresses your question. If not, just let me know.
You have a relation such that .
The range of any relation is the set of second terms.
What is the set of all second terms in ? How is a difference of two reals rational?
Here are examples.
because is rational.
because and zero is rational.
Does that mean that is reflexive?