Hello,
I would like to pose a question concerning the definitions for the functions mentioned in the title.
In my book I found the following definitions:
Function- A relation R from A to B is a function iff:
1) Each element in the domain is paired with just one element in the range.
2) The domain of R is equal to A.
Surjective onto function-
If every element in the range is paired with at least one element in the domain.
Injective one to one function-
If every element in the range is paired with exactly one element in the domain.
Bijective function-
Both Surjective and Injective.
Now here is the question:
Is the example for an injective function that is not Surjective and therefore not Bijective achieved when there are more elements in the domain than in the range? Are there any other possibilities for having an injective function?
Than for example we have A= { a, b, c} B = { 1, 2}
And a and b are paired with 1 whereas c with 2.
That's a function because every element of A is paired with one element of B. That surjective because every element of B is paired with at least one element of A.