Equivalence Relations and Partitions

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We look at the connection between equivalence relations on a set and partitions of a set.

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8:18 Find someone who loves you as much as Michael loves the floor function.
17:46 Good Place To Stop

goodplacetostop

just came across this video for a discrete math class i am taking- super helpful btw!. i could not help but notice your build- i had a feeling like you were a hiker, cyclist, or rock climber and sure enough, you are an OG rock climber. thanks for the math content and keep shreddin out there man

jairusmartinez

Thanks! I've been looking for a video on this for some time

jamesyeung

For the converse, just say xRy if and only if they are in the same partition and prove that indeed it is an equivalence relation.

jimallysonnevado

3:36 it's amazing how Michael can erase the board with just one tap. Mathematical superpowers ?

sapientum

I'm posting this before I swatch because it is a meta-question.
How come on this video, the other equ-video, and some others the video is smaller than usual?
The similar videos on the right take up almost half the the screen - left/right - while the are normally about a quarter.

pauljackson

It would help me to give an example before the generality. It help me visualize. Eg the domain is complex numbers the equivalence relation is the norm ie r when z=r.exp(i.theta).
So [z] is a circle radius r centred at the origin of the argand diagram.

davidseed

2:25 Why not just take x in [x]=[y]? Then you’re done.

noahtaul

Hi: I seem to have missed "The previous video".

It's here, for anyone else who missed it and wants to catch up:

And while I am here I will also suggest that whenever you have a follow on video is helpful to post the link in the description; and to post a forward link in the description of the previous one.

Warmly :)

trueriver

I would like to share a matter of geometric probability Three friends set up a meeting in front of the Nilton Santos stadium to watch a a soccer match. They agreed that each one should arrive in a moment chosen between 3 p.m. and 4 p.m. and that none of them will wait more than 30 minutes for too much, within the stipulated time. What is the probability that the three friends will meet between 3 p.m. and 4 p.m.? Answer : 1/2

martinsangelo

What if A is the empty set?
Then we can’t guarantee that P is nonempty
So we should specify A is non empty

Happy_Abe

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