I can't help but wonder why I pay thousands of dollars for university tuition if my stupid textbooks can't explain things as easily as many of the wonderful videos by people such as yourself. Thanks so much for this!
All these lectures in uni about this and I go to one 6 minuet RU-vid video which explains something I failed to grasp in an hours lecture. You sir are fantastic! You made it simple and easy to understand.
My textbook says: "To find the equivalence class of every element of A, do this: [0] = {x E A | xR0 } = {0,4} [1] = {x E A | xR1 } = {1,3} [2] = {x E A | xR2 } = {2} ..... and so on." I have no idea what the author is talking about. I do not understand why some professors do not use simple English to express some new concepts. Your video makes it so easy for me to understand what Equivalence Class really is. For that, I say thank you.
Agreed. The authors of these textbooks are much to pompous and arrogant to realize who their audience is. They thought they would be winning a nobel prize in their youth and now take out their anger for their failures on university students trying to learn. Shame on them. I'm not going to get the job app for the free game tickets for the game tickets for my tickets and I don't get it because they don't get tickets to get the game tickets for tickets I want tickets and they will and I have a big ticket for a Christmas present and they don't have to be there when I'm leaving for Christmas because they are not going to be there because they are so big they have to come back with the squad they don't are there for Christmas they 🎄 with the a frat house that is a big bag security for a man to get a free game tickets for Christmas Day and the game tickets for Christmas Day and they will a frat ticket for yuyyour and the squad they have tickets to get tickets for tickets tickets to Christmas and Christmas Eve is going on a super smash ticket for Christmas and they are going out of their way and he came tickets to Christmas and Christmas dinner for Christmas present and tickets are on their team comes on
I've spent 5 days trying to understand how equivalence classes actually work, you just taught me in five minutes. Super helpful video and detailed video. Thanks alot!
Thank u sir....I've been trying to study it for an hour now....my textbooks are making it complex...but u explained in in the most simple way...thank you
Thank you for taking the time to make these videos. Such a fundamental concept, yet very few (if any) books clearly explain these concepts with examples as good as these.
I thought equivalence classes are all disjoint? [Edit:] Wait nevermind, the equivalence classes of [1], [2], and [3] are all equal, so they are the same equivalence class.
Whenever you need to prove equivalence relations, just show that the properties of reflexibility, symmetry and transitivity hold. For this example: Reflexibility. m-m=0 is divisible by 7, hence mRm holds Symmetry. If m-n is divisible by 7, then so is n-m (since n-m = -(m-n) ), hence mRn -> nRm holds Transitivity. If mRn and nRa, then 7 divides both m-n and n-a. 7 then also must divide their sum. (m-n) + (n-a) = m-a, hence mRn
