I need to prove that there exist a one-to-one function: $\displaystyle f:A\rightarrow A\times B$

where should i start?

thanks in advanced!

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- Dec 14th 2012, 01:30 AMStormeyone-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?

thanks in advanced! - Dec 14th 2012, 02:39 AMDevenoRe: 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 AMStormeyRe: 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 AMPlatoRe: one-to-one function
- Dec 14th 2012, 08:05 AMemakarovRe: 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 AMStormeyRe: one-to-one function
Thanks guys.

appreciate it!