# one-to-one function

• Dec 14th 2012, 01:30 AM
Stormey
one-to-one function
I need to prove that there exist a one-to-one function: $\displaystyle f:A\rightarrow A\times B$
where should i start?

• Dec 14th 2012, 02:39 AM
Deveno
Re: one-to-one function
try picking a function that maps an element a to (a,___) (i'll leave it to you to decide what might go in the blank).
• Dec 14th 2012, 06:56 AM
Stormey
Re: one-to-one function
do i just need to provide an example of a function that goes from $\displaystyle A\rightarrow A\times B$?
(like $\displaystyle (a, (a, b))$ or $\displaystyle (a, (a, d))$...)

im not sure what exactly do i need to prove here...
• Dec 14th 2012, 07:09 AM
Plato
Re: one-to-one function
Quote:

Originally Posted by Stormey
do i just need to provide an example of a function that goes from $\displaystyle A\rightarrow A\times B$?
(like $\displaystyle (a, (a, b))$ or $\displaystyle (a, (a, d))$...)

im not sure what exactly do i need to prove here...

'Fix' a $\displaystyle b\in B$. Then define $\displaystyle f:A\to (A\times B)$ by $\displaystyle a\mapsto (a,b)$.

Now prove $\displaystyle f$ is one-to-one.
• Dec 14th 2012, 08:05 AM
emakarov
Re: one-to-one function
And note that the original claim is false when B is empty but A is not.
• Dec 15th 2012, 05:32 AM
Stormey
Re: one-to-one function
Thanks guys.
appreciate it!