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 Post subject: Re: Functions on Arbitrary Sets and Groups
PostPosted: Thu, 1 Mar 2012 00:45:49 UTC 
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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 Groups
PostPosted: Thu, 1 Mar 2012 00:53:29 UTC 
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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 Groups
PostPosted: Thu, 1 Mar 2012 01:02:37 UTC 
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You are right about it being injective, but you have to follow the definition of injectivity and that is "if f(x) = f(y), then x = y.

so in this case you must start with f(a) = f(a') and end with a = a' for some a, a' \in A.

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 Groups
PostPosted: Thu, 1 Mar 2012 02:49:17 UTC 
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daveyinaz wrote:
You are right about it being injective, but you have to follow the definition of injectivity and that is "if f(x) = f(y), then x = y.

so in this case you must start with f(a) = f(a') and end with a = a' for some a, a' \in A.

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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