Math

Injective (one-to-one) functions send different arguments to different values; in other words, if x and y are members of the domain of f, then f(x) = f(y) only if x = y. Our function above is injective.

Surjective (onto) functions have their range equal to their codomain; in other words, if y is any member of the codomain of f, then there exists at least one x such that f(x) = y. Our function above is not surjective.

Bijective functions are both injective and surjective; they are often used to show that the sets X and Y are "the same" in some sense.

more on it.......

Let S and T be nonempty sets.

f:S -> T is an injective function if f(s1) = f(s2) implies s1 = s2.
(This is often called a "one-to-one" function.)

f is a surjective function if for all t in T, there is an s in S
such that f(s) = t. (This is often called an "onto" function.)

f is a bijective function if it is both injective and surjective.
(This is often called a "one-to-one correspondence".)

The difference between the definitions you found is not in the two
phrases you picked out, which are, indeed, synonymous. It is,
instead, in the parts immediately preceding them. Let me rephrase
them to see what I mean.

A function f:S -> T can be thought of as the set of all ordered
pairs F = {(s,f[s]): s in S}, which is a subset of S x T. (This
set F is often called the graph of f.) It is a function if and
only if each element s in S appears exactly once as the first
component of an ordered pair in F.

it is all copied from net becoz i dont have enuf time to type......still if doubt persists in ur mind,scrap me and i will try to explain it further[1][1]