Basic abstract algebra, pt.3

This will be a video series about basic abstract algebra and group theory. We will keep it basic so that anyone can follow the videoes.

This is the third video in the series, and we will look at an example of a group. We also find an example of something that is not a group.

Category:

Education

Tags:

• basic
• abstract
• algebra
• group
• theory
• mathematics
• math
• theorem
• prove
• proof
• binary
• operator
• science
• function
• set

[mnhtapu]

Great job!

Name of proof method : Reductio ad absurdum

Mechanics: Assume opposite, get a ridiculous/ contradictory result.

[rehcaethtam]

Dear VeritySeeker.

Thanks for your efforts to make those useful videos about abstract Algebra.

For the time being, I've read part 1 to 3.

I will continue studying the whole video series.

To understand more abstract algebra is one of my dreams, and so thank you very much again.

Math learning and teaching mania

rehcaethtam

[feanor607]

@tqoftu1 Definitely helped me - with thanks to ALL.

[slherman9205]

Thanks for the videos! these are really going to help on my test!

[tqoftu1]

@cmonington Since we have 2*x = 3 and (a*b) = a*a*b*b, we can rewrite the first 2*x as 2+2+x+x=3 which can be rewritten as 4+x+x=3

4+x+x+-4=3+-4

x+x=-1

So clearly the only solution is x=-1/2

I hope this helps.

[VeritySeeker]

@Aishasiddiqa100 What claim?

[VeritySeeker]

@johnwpurcellx Thanks, mate. If someone can watch this on a Saturday evening and have something to think about on Monday, well - then I am happy ;).

[Aishasiddiqa100]

can u give me a general proof for ur claim

[Aishasiddiqa100]

can u give me a (general) proof of ur claim

[cmonington]

In the last part of the video, how does 2*x=3 where (a*b)=a*a*b*b and x = -1/2. I don't understand how x=-1/2. Can anyone explain this please.

[pbajaj5]

Thanks so much, you rock!!!

[RurouniDizeru]

@gorgolyt so i didn't know that conditions for properties were sometimes called axioms. but i accept that now.i realise something.if i really didn't now what i was talking about then why did VeritySeeker agree with me when i explained what i meant?think about that