LOGIC Functions Defined on General Set?

Question

Student C tries to define a function h:Q --> Q
by the rule:

h(m/n)=(m^2)/n, for all integers m and n with n not equaling 0.

Student D claims that h is not well defined. Justify Student D's Claim.

Answer 1

The value of h is dependent on the representation. For instance, even though 1/2 = 2/4, we have h(1/2) = 1²/2 = 1/2 ≠ 1 = 2²/4 = h(2/4). Therefore, h is not well-defined.