Kyle C.

# Prove that the function f : Z ? N defined by f(x)=(|4x+1|+1)/2 is injective

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Kyle C.

Thank you so much Arnold! S
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03/08/16

Kyle C.

So just to be sure this means its not injective right? Do I need to do all the cases if the first case proves its not injective?

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03/08/16

Arnold F.

I believe it is injective:

1. For case 1 above to be true:  4x+1=4y+1 so x=y (this is what we needed to show for injective to hold)

2. For case 2 the same

3. Cases 3 and 4 can't happen, that is the inside of the abs val can't be negative in one and positive in the other and still be equal (try it out.)

So the result is: if f(x)=f(y) then x=y.

Let me know if this makes sense to you.

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03/08/16

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