How to Prove a Set is a Group

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Hi @TheMathSorcerer.... Your video clearly explains most of the properties or axiom for a Group to exist.
However, you did not include the axiom of the closure property which is essential to seal that a group does exist.
Looking forward on your clarification and the steps needed to proof this

SupraManiam

What an awesome explanation!!!
English is not even my mother tongue (spanish) and i understood this pretty well.

This is quite better than my current teacher's explanations

Angel-VTek

Thank you for this detail explanation Sir.

renolphilip

Great Work! I have been adding the side work as part of the proof and i think my Professor has just been tolerating it LOL

tmendoza

Thank u so much. I watched this and solved my assignment question very easily.

anatinaiemah

Great stuff.
It is hard to find content on this, not to mention good content.
Thank you for your work!

DejaimeNeto

Thanks a lot, amazing explanation suitable for all cases

ОлександрОлександровичНовік

If G and H are two sets that are bijective with each other and there exists a binary operator for G making G a group then there exists a binary operator for H making H a group that’s isomorphic to G

cameronspalding

Dear sir, how to guarantee that the identity element you found is the only one i.e. unique?

sayanjitb

I was under the impression that we must prove the operation is a binary operation to prove a set it a group. Is that not true?

morgandevlin

When you proved the associative property you assumed the resulting expression was commutative. Can you do this?

zeronebula

That was really instructive great sorcerer, many thanks :)

ozzyfromspace

a, b€ IR - {1} = W, say
Then, ab€ W
a€ W => a^ (-1) € W.
Your procedure is unique ✅

SubradipChakraborty

some of the symbols you use are confusing to me as we do not use most of them at school!

RaikaCODM

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