Equivalence Relations - Reflexive, Symmetric, and Transitive

A relation that is all three of reflexive, symmetric, and transitive, is called an equivalence relation. Reflexive means that every element relates to itself. Symmetry means that if one element relates to another, the same is true in the reverse. Transitive means that if a relates to b, and b relates to c, then a relates to c. When all three are true AT EVERY POINT then we call it an equivalence relation. For example, equality of numbers is an equivalence relation.

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[katbutler]

it feels like you're kindly yelling math at me which is probably the only way I'd learn this, so thank you

[chrismcbride]

Great explanation, great channel.


..is your hand pink?

[hello_namoo]

imagine my professor can explain this simple topic within 5 mins

[blairdelarosa]

Thanks for explaining, im struggling in abstract algebra and this cleared up alot!

[Heccinchonker]

the fact that you are writing all this backwards so we can read it well behind the glass is very much appreciated

[vamunki]

Caught red handed at being a good explainer

[fonzie]

Thank you so much for the explanation. Great job

[Lena-ofwd]

Great explanation this was helpful, thank you!

[merlinpunnoose]

You are a brilliant teacher...God bless you

[solomonirailoa]

Thank you sir. Do you consider making an Abstract Algebra playlist?

[MineCrafterCity]

Is there a video about antisymmetric relationships?

[oximas]

what's an example of non equivalent relations?

[happypandaface]

isn't your second example with modular arithmetic just explaining the equality operator again? using this explanation, you can use the equality operator to prove that any other operator is an equivalence relation... which seems wrong.

[lovestonthebeat]

Thanks, , RUSHING OFF TO THE EXAM IN 30M

[aner]

Hi :) I'm a math student, and I'm trying to understand for really long time, why if a relation has those 3 conditions (ref, sem and trans..), he called as "equivalnce relation"? Why are we saying that if xRy so x is equivalent to y ? Where that name came from ? For me thay are just relate to each other but why they are equivalent ? Thank you.

[lukemiller]

This shit makes no sense I’m failing my final rn

[xobk]

In my book we have questions like:
x is related to y if y ≥ x+1. The domain is the set of all positive real numbers. Is this Transitive or Not Transitive?

And the answer is:
If y ≥ x+1 and z ≥ y+1, then z ≥ x+2 which implies that z ≥ x+1. Therefore the relation is transitive.

I feel like I get the concept, but the problems aren't making sense. I cannot figure out how I am supposed to assume the value of z, or that it even exists. They do not pose that "z ≥ y+1" in the question. So if I am testing values for x, y, and z, I could set x=5, y=6, and z=1, then would it still be transitive?

[MathCuriousity]

Can you explain what you mean by the equality operator representing something different in the mod arithmetic example compared to the integers example? I don’t see how the equality operator is any different in mod arithmetic? Please crystallize this hidden knowledge you have attained!

[archanavarun]

I'm still scratching my head, how could you write, mirror language, so consistently??

[eyzhie]

Is nobody going to talk about how he is actually writing backwards?