lime wrote:x -> 2x is also "onto" and "one-to-one", isn't it?
f(x+y) = f(x) + f(y) for x,y ε Q iff for ax + b, b = 0; also, if f is just an additive group isomorphism from Q onto Q, then a would trivially be 1. Isn't this a practice test question? I recall originally thinking Q had ∞ automorphisms then rethinking that it must only be 1.
Return to “Mathematics GRE Forum: The GRE Subject Test in Mathematics”