# Proving a function is one-to-one/onto

• October 5th 2009, 03:57 PM
Projectt
Proving a function is one-to-one/onto
I have a function:

$f(m,n) = mn$

The domain for this is $Z \times Z$. The range is $Z$. How can I prove if it is one-to-one, onto, or both?
• October 5th 2009, 04:08 PM
Plato
Quote:

Originally Posted by Projectt
I have a function:
$f(m,n) = mn$
The domain for this is $Z \times Z$. The range is $Z$. How can I prove if it is one-to-one, onto, or both?

It is clearly not one-to-one: $f(2,3)=f(3,2)$.
Is it onto? If $z\in \mathbb{Z}$ then is it possible that $f(?,?)=z$?
• October 5th 2009, 04:20 PM
Projectt
Ohh, I thought Z was some arbitrary set, not the set of all integers. Thanks.