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Invertibility / Group problem

  1. Apr 16, 2012 #1
    I have to find if the set [itex] [1;+∞[ x [1;+∞[ [/itex] with the operation [itex] (x;y)°(v;w) = (x+v-1; yw) [/itex] is a group

    I have already proven Closure, associativity and Identity but I have some problems with invertibility :)

    The neutral element that I have found is (1;1)

    I did [itex] (x;y)°(x1;y1)= (1;1) [/itex] and I have found [itex]x1=-x+2[/itex] and [itex]y1=1/y[/itex]
    The problem is that [itex]1/y[/itex] is not included in the set if [itex]y>1[/itex]...

    Any advice? Is it a group? Thank you :)
     
    Last edited: Apr 16, 2012
  2. jcsd
  3. Apr 16, 2012 #2

    LCKurtz

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    Use the forward slash "/" to close your tex tags.
    It looks to me like you have answered your own question. Inverses don't seem to be there.
     
  4. Apr 16, 2012 #3
    So it's not a group? :) The text of the homework that the teacher gave us seemed to imply that it was :)
     
    Last edited: Apr 16, 2012
  5. Apr 16, 2012 #4

    micromass

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    Indeed: it is not a group!
     
  6. Apr 16, 2012 #5
    Thanks ;)
     
  7. Apr 16, 2012 #6

    micromass

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    Just so you get it. The problem is that 1/y is not necessarily in our set. But that is not the only problem. There is a problem with -x+2 as well. That also doesn't necessarily lie in our set!! Indeed, if x=2, then -x+2=0 and this is not in our set!
     
  8. Apr 16, 2012 #7

    LCKurtz

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    C'mon. Show a little confidence in your work. Do you want to build a fence around it and insure it before you are willing to assert the result?
     
  9. Apr 16, 2012 #8
    Well, I prefer to be sure about what I write especially if it is on a new topic that I have just learned at school ;) By seeking help and advices on the internet I hope to improve and strenghten my knowledge and thus be more confident. I didn't expect it to be a problem.
     
    Last edited: Apr 16, 2012
  10. Apr 16, 2012 #9

    LCKurtz

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    It isn't a problem; I didn't mean to imply that it was. You nailed it on your first try. I was just trying to encourage you to be brave about what you've done. You do good work, so trust it.
     
  11. Apr 17, 2012 #10
    Thanks, I will :)
     
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