Abstract Algebra | Equivalence Relations

We give the definition of an equivalence relation and some examples.

[Nick-xzng]

I'm loving the instantly cleared board with the snap edit lmao

[hyperduality]

Equivalence (reflexivity, symmetry, transitivity), similarity = Duality.
Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence -- duality.
Integration or anti-derivatives are syntropic processes -- teleological.
"Always two there are" -- Yoda.

[mingmiao]

Wait, is ‘nothing’ a technical term here? Thanks for posting the video!

[brianbutler]

@0:08 The terminology I learned calls AxA a “Cartesian product” and not a “cross product“ when A is a set.

[maxpercer]

6:47 indefinite integral (not improper integral, which is a different concept) . nice video

[MyOneFiftiethOfADollar]

Using the terminology of coarse and fine when showing that equality and "nothing" are equivalence relations HAS to be connected to coarse and fine topology. Coarse was the empty set and fine was that all subsets were designated "open" I think?

One of my favorites: all the points that are same distance from a fixed point form an equivalence relation(R cross R). Oh yeah, that is a circle.

[Glads_nievez]

Thank you for this! It helps me a lot for my presentation this coming week! <3

[manthing]

6:48 Did you mean to say indefine instead of improper? Thanks for an awsome video.☺

[Ravit]

Sir if I completely read the book I will tell you then plz suggest me more books ok sir

[alihaydar]

And they say logicians didnt add anything to Aristotle's logic