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[SOLVED] check if relation is equivalent

issacnewton

Member
Jan 30, 2012
61
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
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
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.