/sci/ - Science & Math

>>11750142
If you understood it perfectly, you can share it with us, right? Alternatively, you can answer these questions:
(1) If [math]a\in S[/math], why is it the case that [math][a]\neq \emptyset[/math]?
(2) If [math]c\in [a]\cap [b][/math], what can you say about [math]a, b[/math]?
(3) What can you say about [math]\bigcup\limits_{a\in S} [a][/math] when we notice that [math]S = \bigcup\limits_{a \in S} \{ a\}[/math]?
Also, notice how 1.2 and 1.3 combine to give you this nice result: there is a bijective correspondence between the equivalence relations and partitions of a given set. For 1.3, what would you say about the following idea? Let [math]\mathscr{P} = \{ P_i\}[/math] be a partition of [math]S[/math]. Define [math]a\sim b[/math] if the elements are in the same partitioning set. I suggest you give this a try and maybe write it out here and we can bul... check it.

>>11750148
No problemo. Modular arithmetic is sort of like looking at the clock. It doesn't matter if you use 12 or 24 hours, as 25=1 anyway mod the number of hours. Hopefully your motivation rubs onto the struggling anon.