Question

What's the difference and connection between function & surjection ?

Answer 1

A function takes a value (say x) and changes to another value(say y). Now each function has it's domain and co-domain.
A set of all values of x, for which a function f(x) is valid, is called the domain of the function f(x). Like the domain of 1/(x-1) is a set of all real numbers excluding 1.
Now we can make a set {C} of numbers such that for all values of x the result f(x) will be present on that set. Then the set {c} will be called the co-domain of f(x). Like {y:-2<y<2} will be a co-domain of f(x)= Sin(x).
Now you can easily see that I've taken my co-domain such that it includes all values of f(x) but not all it's values are a in the result of sin(x). Like y=1.5 is in my set but for no value of x will you get sin(x)= 1.5. So the co-domain can contain more numbers than the function demands.
If a co-domain is choosen such that for every y there exists a x such that f(x)=y, then it's called a surjection or surjective function. Otherwise it's just a function not surjection.

Answer 2

then you are saying the co domain will be the same as the domain ,which would make a SURJECTION A FUNCTION.

Answer 3

No..no. Co domain may and may not be same as the domain but co-domain must not include any extra point than those which are values of f(x) in the case of Surjection.
Say f(x) =5. here domain can be set of real no. or set of natural no. but the co-domain has to be {5} only to call it surjection.

Answer 4

Thx, I know these concepts now :-)