Exercise
172
[1YM]Prerequisites:[01R],[(3.171)],[24V]. 1 Prove that
\[ x=y \iff S(x) = S(y) \quad . \]
In particular this shows that, if \(A\) is an S-saturated set, then the function \(S:A→ A\) is well defined, and its graph is the relation
\[ \{ (x,y)∈ A^ 2 : y=S(x) \} \quad ; \]
moreover \(S\) is injective.
Solution
1