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 Post subject: Re: Functions on Arbitrary Sets and GroupsPosted: Thu, 1 Mar 2012 00:45:49 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
For dummies like me, that example helped me out GREATLY! i was finally able to visualize this problem.

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 Post subject: Re: Functions on Arbitrary Sets and GroupsPosted: Thu, 1 Mar 2012 00:53:29 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
looking back now for #3, i initially said it wasn't injective, but every element in A would have a unique image in AxB wouldn't it?

i could show?
if f(x)=(x,b) & f(y)=(y,b)
then we see x=y
so (x,b)=(y,b)

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 Post subject: Re: Functions on Arbitrary Sets and GroupsPosted: Thu, 1 Mar 2012 01:02:37 UTC
 S.O.S. Oldtimer

Joined: Sat, 16 Aug 2008 04:47:19 UTC
Posts: 208
You are right about it being injective, but you have to follow the definition of injectivity and that is "if , then .

so in this case you must start with and end with for some .

Really the hard part is putting into words what comes out in the middle...

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 Post subject: Re: Functions on Arbitrary Sets and GroupsPosted: Thu, 1 Mar 2012 02:49:17 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
daveyinaz wrote:
You are right about it being injective, but you have to follow the definition of injectivity and that is "if , then .

so in this case you must start with and end with for some .

Really the hard part is putting into words what comes out in the middle...

I disagree, the definition is definitely one way to do this, but you can also easily produce a left-inverse as well.

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