In the first example, the word coset was never used. I gather that 1 + 4Z is a coset of 4Z in Z with 1 as representative. Otherwise, very clear and engaging.
It's too late now but just so you know the orange and yellow look very, very similar on video (720p). Even 1080p it looks almost identical. I wouldn't have even noticed if you didn't point it out! Might be best to pair different colours for the future :p
Left cosets are dual to right cosets = commutation or Abelian. Isomorphic subgroups are dual. Injective is dual to surjective creates bijective or isomorphism. Prime numbers are groups with two elements, the identity and the prime number itself. Prime number groups are therefore dual. Spinors: The spin up projector is dual to the spin down projector -- Klein bottle. "Always two there are" -- Yoda. Duality creates reality!
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Sometimes it's funny and cute when he breaks up but never edited it out.
Only a mathematician can make adding zero fill up an entire line on a blackboard.
yeah i was thinking that haha
Excellent video series so far. But how did 4 get into the coset 2 + 4z ? (2:17)
It shouldn’t be there. It should be -2, 2, 6, 10
thank you very much for these amazing videos
yo i finally understand cosets thanks so much, and i get the partiniintoning part as well woooo
love your videos!
sir, you have saved me
thanks for the great job sir
In the first example, the word coset was never used. I gather that 1 + 4Z is a coset of 4Z in Z with 1 as representative. Otherwise, very clear and engaging.
02:16 What's wrong with 2 + 4Z, boys and girls?
It should be {... -2, 2, 6, 10 ...} son.
It's too late now but just so you know the orange and yellow look very, very similar on video (720p). Even 1080p it looks almost identical. I wouldn't have even noticed if you didn't point it out! Might be best to pair different colours for the future :p
something is wrong with U(12) sir??? not sure but why you did not consider the cosets of 5
5 =
Left cosets are dual to right cosets = commutation or Abelian.
Isomorphic subgroups are dual.
Injective is dual to surjective creates bijective or isomorphism.
Prime numbers are groups with two elements, the identity and the prime number itself.
Prime number groups are therefore dual.
Spinors: The spin up projector is dual to the spin down projector -- Klein bottle.
"Always two there are" -- Yoda.
Duality creates reality!
good examples of cosets
i am a little bit confused with how he writes z...
thanks for the great job sir