I have a question regarding the discussion of functions on the set theory handout (page 6).
It says "f(x) is in f(S) <==> x is in S"
Let S = {-1, 0, 1, 2}
and f(x) = x^2
so f(S) = {0, 1, 4}
Counterexample: f(-2) is in f(S) but -2 is not in S
Is this is an error in the notes or have I done something wrong here?
.ps
I tried to find a similar counterexample to the later statement
"f(x) is in U <==> x is in f^-1(U)"
But I couldn't, since it says "f(x) is in U" rather than just "y is in U"