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I proved this inequality ;

Which is a relation on $\mathbb{Z}$ s.t a and b belongs to $\mathbb{Z}$

$$a^2 - b^2 \le 7$$

is reflexive , I'm stuck at the symmetry of this relation, can anyone help? Thank you so much!

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closed as unclear what you're asking by Martin R, Graham Kemp, Yanior Weg, José Carlos Santos, Shailesh May 18 at 3:13

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    $\begingroup$ Your question is unreadable. What is the relation? Who is Abraham? $\endgroup$ – Matthew Leingang May 16 at 10:04
  • $\begingroup$ Are you sure this defines an equivalence relation? $\endgroup$ – P-addict May 16 at 10:08
  • $\begingroup$ I'm so sorry , I just edited it $\endgroup$ – lasan manujitha May 17 at 11:28
  • $\begingroup$ No we have to check and see if it is , thank you @P-addict $\endgroup$ – lasan manujitha May 17 at 11:30
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The relation is not symmetric. For example we have for $a=0$ and $b=3$:

$a^2-b^2 =-9 \le 7$, but $b^2-a^2=9 > 7.$

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  • $\begingroup$ yes, thank you sir , but how can we prove that for all Z ?, without giving an example $\endgroup$ – lasan manujitha May 17 at 11:29
  • $\begingroup$ He proved that it is NOT an equivalence relation. One counterexample is enough, you don't need to prove it for all $a, b \in \mathbb{Z} $. $\endgroup$ – cavallo rosso May 17 at 11:53
  • $\begingroup$ oh thank you so much @cavallorosso $\endgroup$ – lasan manujitha May 17 at 15:51

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