Hey guys I can't figure out this question.

let f:A->A be a function fof is injective

Prove wether f is injective or not

Can someone show me what's the proof

THANKS !

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- Sep 15th 2012, 12:33 PMBurcinIs f injective or not?
Hey guys I can't figure out this question.

let f:A->A be a function fof is injective

Prove wether f is injective or not

Can someone show me what's the proof

THANKS ! - Sep 15th 2012, 12:43 PMPlatoRe: Is f injective or not?
- Sep 15th 2012, 01:00 PMBurcinRe: Is f injective or not?
yes it follows because f(a)=f(b) so I see that fof(a)=fof(b)

I cant see the next step - Sep 15th 2012, 01:05 PMPlatoRe: Is f injective or not?
- Sep 15th 2012, 01:14 PMBurcinRe: Is f injective or not?
oww I see it so a is not the same as b so f isn't injective is it right?

- Sep 15th 2012, 01:21 PMPlatoRe: Is f injective or not?
- Sep 15th 2012, 01:50 PMBurcinRe: Is f injective or not?
YES I understand! Thank you very much !

- Sep 15th 2012, 02:16 PMPlatoRe: Is f injective or not?
This one of a group of three part theorem.

Given any functions $\displaystyle f~\&~g~:$

a) if $\displaystyle g\circ f$ is injective then $\displaystyle f$ is injective,

b) if$\displaystyle g\circ f$ is surjective then $\displaystyle g$ is surjective,

c) if $\displaystyle g\circ f$ is bijective then $\displaystyle f$ is injective and $\displaystyle g$ is surjective. - Sep 15th 2012, 02:48 PMemakarovRe: Is f injective or not?
There is a typo in b).

- Sep 15th 2012, 11:22 PMBurcinRe: Is f injective or not?