Basic abstract algebra, pt.14

[Emperorlawson]

I've found in my undergraduate math studies that a small dry erase board w/ some markers is an invaluable study tool. Beats burning a hole in paper with an eraser lol.

[ironclownfish]

Great videos!! I was confused at first though when you were defining cosets. The vertical "such that" line looks like the line you used for "divides". As in 4|8

[Ezzyman17]

Around 2:55 you say that "It is possible that to prove that..... H in G" and then suddenly it changes to G in H? Maybe just a mistake or i don't understand it?

[colverjustin]

im hoping when you said the same remainder when dividing by n!, that the ! is purely an exclamation

[VeritySeeker]

@colverjustin I hope so too ;). Yes, you're right.

[jimmydu444]

mind = blown

[1gombro]

indeed! that's great. one of the most enjoyable and comprehensible videos on the server. At the vert beginning the music seemed a bit disturbing but now I cannot image any other music played here:)

[MinGophers]

more more more! I love em!

[dagln0x0]

I have a little question. As you can see in Lang's book "Analysis (3.ed)" there is an interesting way of giving a group the structure of a topological space (it is called the profinite topology: this topology only involves cosets and subgroups that's why I'm posting here). My question is what kind of results can you prove using this topology.

[interted]

i'm having trouble understand the notation you use for defining sets: ex. gH={gh|hЄH}. First I thought that | meant divides, but now I see that it is equal to : as it appears in my book, which means "as this statement stands". Am I right?

[VeritySeeker]

Hi, yes you are right. A way to read it is like this:

{gh | h in H}

All of the form gh such that h is in H.

I read | as "such that".

So it would be every element that is equal to gh for some h in H. Or... all gh, as h runs through H. Many ways to think of it, and pick the one you prefer.

Yes you are right it is the same as : in your book. Some use that notation aswell.

[magestaff567]

Thanks again for making these great videos. This video has the hardest concepts so far. It really helps!

[ddelphi09]

thank you very munch......such an awesome video....very useful

[sujandeeds]

You are doing great job with this series VS ...  Thank you :)

[IndraniDawn]

awesome..

thank you

[KelvinNg88]

I'm still following. Your series is great. Please don't stop :)

[Semidicht]

Yay! :)

[TheBlackwaterDemon]

Looking forward to more!

[humby123]

Brilliant. Don't stop making these or we will just have to go back to seeing monkeys drink their own urine.