Hello; today my Precalculus teacher gave this definition for the set of rational numbers:

$\displaystyle Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$

Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?

Shouldn't it be:

$\displaystyle Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$

or

$\displaystyle Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?

Thanks,

yottaflop