Check if relation is equivalent

[issacnewton]

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]

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.

 

[issacnewton]

Yes. This is good.

Thanks
(Emo)