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The relation $R:= \{(x,y) \mid y= \vert x\vert \} \subseteq \mathbb{Z} \times \mathbb{N}$ is a function, but the relation $R:= \{(y,x) \mid y= \vert x\vert \} \subseteq \mathbb{N} \times \mathbb{Z}$ is not a function...

for me it seems that the second relation has also those two properties 1. total left and 2. right-unique....According to my book I´m wrong :) maybe a hint would help...thx

Googme
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1 Answers1

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For the second $R$ notice that you have $(1,-1)\in R$, $(1,1)\in R$ which is against "right-unique".

Emanuele Paolini
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  • hmm, I thought that y is \in \mathbb{N} and x is in \mathbb{Z} so every time I have a negative integer the absolute value of x is going to transfrom it. – Googme Jan 01 '14 at 11:45