/sci/ - Science & Math

It's not that I'm dumb. I'm just alternatively intelligent!

>>12209421
Hi.

>>11749783
Letters indeed. If you want a more mathsy example, so be it. Do you know modular arithmetic? Choose some positive integer [math]n[/math]. We can then define [math][a]_n = \{ b\in \mathbb{Z}\ |\ b \equiv a\text{ mod }n\}[/math] (congruence mod [math]n[/math] is an equivalence relation). These sets are the equivalence classes of the congruence relation. Next, notice that if [math]a\equiv b, c \equiv d \text{ mod }n[/math], then [math]a+c \equiv b+d \text{ mod }n[/math]. It follows that we have an addition for the equivalence classes: [math][a]_n + [c]_n = [a+c]_n[/math], and this actually leads to a group structure (and gives the group [math]\mathbb{Z}/ n\mathbb{Z}[/math]). This idea generalises to all quotient groups.