同余关系和等价关系有什么区别？

〜是全等关系，如果

$for a, b, c, d in $G$, if $a$~$b$ and $c$~$d$ then $ac$~$bd.$$

$This is useful to define normal subgroups, and quotient groups because G/~ is a group with a binary operation that respects the congruence relation.$

$There are two relations known as congruence relations. One is in geometry and refers to congruent figures. Two figures are congruent if there is a rigid motion that moves one to the other. The other is in number theory and refers to integers congruent modulo n where $n$ is some fixed integer. Two integers are congruent modulo $n$ if their difference is divisible by $n.$ This second congruence relation has been extended to elements of a ring modulo an ideal.$