<Dl> <Dd> f: A → (0, 1) (\ displaystyle f: A \ rightarrow \ (0, 1 \)). </Dd> </Dl> <Dd> f: A → (0, 1) (\ displaystyle f: A \ rightarrow \ (0, 1 \)). </Dd> <P> Whereas the definition in step 1 . is formulated with the freedom of any definition and is certainly effective (without the need to classify it as "well - defined "), the assertion in step 2 . has to be proved: If and only if A 0 ∩ A 1 = ∅ (\ displaystyle A_ (0) \ cap A_ (1) = \ emptyset), we get a function f (\ displaystyle f), and the f (\ displaystyle f) of "definition" is well - defined (as a function). </P> <P> On the other hand: if A 0 ∩ A 1 ≠ ∅ (\ displaystyle A_ (0) \ cap A_ (1) \ neq \ emptyset) then for an a ∈ A 0 ∩ A 1 (\ displaystyle a \ in A_ (0) \ cap A_ (1)) there is both, (a, 0) ∈ f (\ displaystyle (a, 0) \ in f) and (a, 1) ∈ f (\ displaystyle (a, 1) \ in f), and the binary relation f (\ displaystyle f) is not functional as defined in Binary relation #Special types of binary relations and thus not well - defined (as a function). Colloquially, the "function" f (\ displaystyle f) is called ambiguous at point a (\ displaystyle a) (although there is per definitionem never an "ambiguous function"), and the original "definition" is pointless . </P>

When can you say that a set is well-defined