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

1. Jul 22, 2011

### gotjrgkr

1. The problem statement, all variables and given/known data
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).

2. Relevant equations

3. 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??

2. Jul 22, 2011

### tiny-tim

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

3. Jul 22, 2011

Re: function

Thank you!