## Mille poolest erinevad kongruentsussuhe ja ekvivalentsussuhe?

Vastus 1:

David Joyce'i vastus on hea, kuid seal on veel üks kongruentsuse suhte määratlus, mida ma olen näinud (Hungerfordi algebra):

Olgu G monoid ekvivalentsussidemega ~.

~ on kongruentsussuhe, kui

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

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

Vastus 2:

$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.$

Mõlemad on ekvivalentsussuhted. Võib esineda ka teisi ekvivalentsussuhteid, mida nimetatakse kongruentsussuheteks.

Teie küsimusele vastuse saamiseks on kongruentsussuhe konkreetne ekvivalentsussuhe, mida on hakatud nimetama kongruentsussuhteks.