Kickin’ it with Partitions and Such

We started Monday’s class off with talking about the final, which is going to be a scavenger hunt.

Then Casey picked people (let them volunteer) for the POW Kick Hug Challenge, and I didn’t have to do it!

But then I had to watch other people do it, which would affect my grade on it.

But then we totally won and we all got perfects on it (wasn’t even surprised).

But after that adventure, we had to go back inside and think about FOMy things.

But it’s all good, partitions are pretty cool.

We talked about how you can go back and forth from partitions to equivalence relations as long as you know one of them to start out with. It’s really all about using different notations and knowing what they mean.

In the book they use this fancy C looking thing, but I’ll just use C. This C thing is the set of all subsets that S is partitioned into. So, when you’re thinking about say, M&Ms. If you split them up by color to eat them (weird, why would you do that, but no judgement), C would then be all the sets of colors you have split them into.

We then started talking about the other confusing notation in the book, and related it to concepts we’d already learned about.

Ct= {z ∈ S: z~t} = [t] (the set of equivalence classes that in a given set S)

x~y= (∃ u∈C)(x,y∈U) (~c  is always transitive, symmetric and reflexive)

Welp. That’s it.


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