No, that is the definition of "function" itself. Further, sqrt(x), as a function, is defined as " is thepositivenumber, a, such that . is NOT equal to -4 by the standard definition.

Now THIS is the definition of "injective". But your "example" is of a function that is NOT injective.2) X1≠x2 -> f(x1)≠f(x2) Ex: 2^{2}=(4), (-2)^{2}=4

(3) is good. (4) is just the definition of "function".1) and 2) imply the alternate definition:

3) f(x1)=f(x2) -> x1=x2

4) f(x1)≠f(x2) -> x1≠x2

Again, (1) and (4) are necessary that the relation be a1) & 4) are equivalent.

2) & 3) are equivalent.

Any of the combinations (tests) 1),2); 1),3); 4),2); 4),3) establish an injection.functionand "injective" and "surjective" are only defined for functions.

Equivalently, f:A->B is "surjective" if and only if, for any b in B, there exist a in A such that f(a)= b.Surjective is relative:

If B=f(A), f:A->B is surjective. (if f is also injective, called bijective, or 1-1 onto,)

If B=f(A) is a subset of C, f:A->C is not surjective. (if f is injective, called 1-1 into,)