Why at 1:55 do we have to prove the inverses of the right coset instead of the inverse of the left coset? Are we making the assumption that H is normal so both left and right cosets are the same?
The original statement of (4) can be proved by assuming (3) is true: Assume (3) is true. Then g_1=g_2h for some h \in H, which is equivalent to g_2=g_1h^{-1} \in g_1H as h^{-1}\in H. So it is not necessary to modify (4) 🤣
I would love if you could continue this series with Sylow's theorems, fields and field extensions.
This make so much sense and can relate a lot to it and understand what you mean and say
Why at 1:55 do we have to prove the inverses of the right coset instead of the inverse of the left coset? Are we making the assumption that H is normal so both left and right cosets are the same?
I dont know how to demosntrate the final one, I suck at demosntrations
Hey what happened to bprp????
I am not sure. I feel indebted to him for a few shout-outs that really helped my channel.
The original statement of (4) can be proved by assuming (3) is true: Assume (3) is true. Then g_1=g_2h for some h \in H, which is equivalent to g_2=g_1h^{-1} \in g_1H as h^{-1}\in H.
So it is not necessary to modify (4) 🤣
Yeah, sometimes I blank on the proofs while making these videos because I am thinking about other things.
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