MHB Check if relation is equivalent

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The relation defined as \(m \sim n\) in \(\mathbb{Z}\) if \(mn > 0\) is examined for equivalence. It is determined that the relation is not reflexive because the pair \((0,0)\) does not satisfy the condition. Consequently, it cannot be classified as an equivalence relation. The conclusion is affirmed by participants in the discussion. The analysis confirms that the relation fails to meet the criteria for equivalence.
issacnewton
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Hello

I have to check if the following relation is an equivalence relation.
\[m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0\]

I think this relation fails to be reflexive since $(0,0)$ does not belong to
this relation. Hence this is not an equivalent relation. Is this ok ?

Thanks
 
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IssacNewton said:
Hello

I have to check if the following relation is an equivalence relation.
\[m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0\]

I think this relation fails to be reflexive since $(0,0)$ does not belong to
this relation. Hence this is not an equivalent relation. Is this ok ?

Thanks
Yes. This is good.
 
caffeinemachine said:
Yes. This is good.

Thanks
(Emo)
 

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