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Let $A=\{ 2+\frac{1}{n+1} ,\quad -2+\frac{1}{n+1} \mid\quad n=0,1,\ldots \}$.

Find a bijection from $\mathbb{Z}$ to $A$.

I try to set $f : \mathbb{Z} \to A $ where $f(k)=2+\frac{1}{k+1}$ if $k\geq 0$ and $f(k)=-2+\frac{1}{k+1} $ if $k <0 $. But this does not work.

Can you give some ideas?

Thank you!

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    What do you mean by isomorphism?2012-01-18
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    The word "isomorphism" is usually reserved for situations where the sets involved are closed under some operation. Is there an operation under which $A$ is closed? Or are you just asking for a one-one onto map between the two sets?2012-01-18
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    do you mean $f(k)=2+\frac{1}{k+1}$?2012-01-18
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    Do you mean bijection?2012-01-18
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    Yes i mean a one-to-one and bijection map from Z to A.2012-01-18
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    @Pjennings:you are right. I edit it.2012-01-18
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    What is $A$? Is $A$ the set that contains all rationals of the form $2+\frac{1}{n+1}$ and $-2+\frac{1}{n+1}$, with $n=0,1,\ldots,$? I ask because your notation is at best confusing.2012-01-18
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    @ Arturo: Yes that's what I mean. Sorry for the bad notation.2012-01-18
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    @GerryMyerson: Don't forget isomorphisms in the category of sets ;)2012-01-18
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    @Michalis, I had that in mind when I wrote "usually".2012-01-19

2 Answers 2