To check that if this inequality is an equivalence relation on $\mathbb{Z}$

Question

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!

Answer 1

The relation is not symmetric. For example we have for $a=0$ and $b=3$:

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