Thursday, February 21, 2008

In light of my last post


My abstract algebra midterm had a delightful question on it that was just too easy:
If G is a group in which every element is its own inverse, then G is abelian.
(HA! Too easy. I LOVE proving that things are abelian, and this is super easy. Wanna see? Too late!)

NOTE: I am not saying that if you can't do this you are not smart, but compared to other things in group theory I think this is one of the easiest things to do.

NTS. If G is a group in which every element is its own inverse, and then G is abelian.
Proof:
and



We can do the same for b.






Since we can cancel and therefore which shows that G is abelian.
QED.

I also finally just got latex for blogger to work and wanted to use it. Also, I just really liked doing this proof. It's fun, and did I mention easy?
at

13 comments:

  1. Anonymous21/2/08 16:56

    Math joke alert! Check this out:
    http://www.irregularwebcomic.net/1640.html

    ReplyDelete
  2. me21/2/08 21:48

    Funny coincidence: I was doing this exact problem today! It finally occurred to me, after staring at your post in confusion for a while, why we can say a^2b^2 = (ab)^2. Thanks!! Who knew feminism would help me with my math homework?!

    ReplyDelete
  3. lost clown21/2/08 22:14

    left and right cancellation is a wonderful thing. I love proving things are abelian, it's so straightforward.

    Well, this is the blog of a feminist mathematician/physicist. Glad I could help!

    ReplyDelete
  4. Dr. Brazen Hussy22/2/08 04:55

    Dude, I have no idea what any of that meant. You are, like, so much smarter than me.

    ReplyDelete
  5. lost clown22/2/08 11:02

    Yes, because anyone can type and sequence DNA (and do all that other stuff you do that I don't quite understand).

    ReplyDelete
  6. Dr. Brazen Hussy22/2/08 11:04

    DNA sequencing is easy! All you need is an opposable thumb. I'm planning to train a monkey to do my work for me... just as soon as I can find a monkey.

    ReplyDelete
  7. lost clown22/2/08 11:08

    I want a monkey!

    (and what about all that other stuff? hmmmm?)

    ReplyDelete
  8. Dr. Brazen Hussy22/2/08 11:34

    I don't quite understand all that other stuff either. :)

    ReplyDelete
  9. Maggie23/2/08 10:52

    I'm not looking forward to being given formulae like these to work on in my math class this semester! (despite the fact that I passed my final math exam in high school years ago -- it's been a long time)

    For sure there will be a lot of revision and homework to do!

    ReplyDelete
  10. lost clown23/2/08 11:42

    You're studying abstract algebra?

    ReplyDelete
  11. Maggie23/2/08 15:11

    Not at the moment. (*sigh*) At the beginning of my semester, I'm mainly required to work out numeracy and arithmetic exercises. But, I know there will be a re-introduction to algebra at some point (as the teacher mentioned to us). I don't know about abstract algebra. It's been years since I left high school (and BTW there were very hard equations at the final math exam as well as some formulae that looked like the ones in your post - I remember). So, what's the difference between abstract algebra and any other kind of algebra, Lost Clown? What are the other kinds of algebra? Enlighten me!

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  12. Anonymous6/3/08 18:57

    So, I haven't taken a decent math course in years, mostly because I haven't had to. The funny thing is that I get it. I followed along with your proof with no problem. Does that make me a genius. lol. I miss math.

    ReplyDelete
  13. lost clown6/3/08 19:03

    No, it just means you like Algebra. ;)

    ReplyDelete

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