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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Originally Posted by Burcin let f:A->A be a function fof is injective Prove wether f is injective or not Suppose that . Does it follow that WHY? You know that in injective. SO?
yes it follows because f(a)=f(b) so I see that fof(a)=fof(b) I cant see the next step
Originally Posted by Burcin yes it follows because f(a)=f(b) so I see that fof(a)=fof(b) I cant see the next step If is injective and the by definition
oww I see it so a is not the same as b so f isn't injective is it right?
Originally Posted by Burcin oww I see it so a is not the same as b so f isn't injective is it right? is injective so implies . So if then , proving is injection.
YES I understand! Thank you very much !
Originally Posted by Burcin YES I understand! Thank you very much ! This one of a group of three part theorem. Given any functions a) if is injective then is injective, b) if is surjective then is surjective, c) if is bijective then is injective and is surjective.
Last edited by Plato; Sep 15th 2012 at 03:55 PM.
There is a typo in b).
Originally Posted by Plato This one of a group of three part theorem. Given any functions a) if is injective then is injective, b) if is surjective then is surjective, c) if is bijective then is injective and is surjective. We haven't had this at school yet but it will help me to solve more problems! thank you
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