Show that B can't be a proper subset of A

[gotjrgkr]

Homework Statement

Let f be a function on A onto B where B is a subset of A, and f is a one-to-one function.
Now, I want to show that B can't be a proper subset of A( that is, not B$\subset$A. this means B=A).

Homework Equations

The Attempt at a Solution

I attempted to solve this problem. Even though it is not complicated problem, but I don't have an idea how to prove it.

Could you give me a clue or something??

 

[tiny-tim]

Let f be a function on A onto B where B is a subset of A, and f is a one-to-one function.
Now, I want to show that B can't be a proper subset of A

hi gotjrgkr!

if A is the integers and B is the even integers, and if f:A -> B is defined by f(n) = 2n,

then f is onto and one-one, but B ≠ A

 

[gotjrgkr]

Thank you!