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Abstract help!

  1. Sep 23, 2010 #1
    Homework problem stated this:

    Let S={0,1,2,3,4,5,6}
    let * be defined by x*y=max(x-y,0)

    is it commutative, associative, does it have an identity and inverse? help please!

    I put that yes it is commutative and yes for associative, but i'm not to sure they are right becuase the 6 is throwing me off

    for identity i got x*e=x and e*x=x
    x+e=x e+x=x
    e=0 e=0
    so yes it has and identity element of zeero and then i pluged it into x*b=e and b (inverse) came out to be equal to x but idk what to do with the 6!

    please help!
     
  2. jcsd
  3. Sep 23, 2010 #2

    Dick

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    I don't think you are really dealing with the definition of '*' very well. Do an exercise first. What is 3*2 and what is 2*3? Use the definition of '*'.
     
  4. Sep 23, 2010 #3
    ohsorry! i meant x*y=min(x+y,6)
     
  5. Sep 23, 2010 #4
    ohsorry! i meant x*y=min(x+y,6)
     
  6. Sep 23, 2010 #5

    Dick

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    Well, that makes a difference. But now I'm not sure what part is actually confusing you. Sure, 0 is AN identity. As for inverses, what would be the inverse of 1?
     
  7. Sep 23, 2010 #6
    whats confusing me is the 6 in min(x+y , 6). And im not sure how to find the inverse property using the identity element

    were the first 3 right?
     
  8. Sep 23, 2010 #7

    Dick

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    Yes, I think the first three are right. I don't see why the '6' is confusing you. min(x+y,6) is the minimum of the number x+y and the number 6. Yes, the identity is 0. So if x is an inverse of 1 then it must satisfy x*1=0. Is there such an x?
     
  9. Sep 23, 2010 #8
    umm well x times 0 equals 0 but if we are saying x*1 as the operation then the only one after plugging it into x+y=0 is -1

    i dont know if that made sense
     
  10. Sep 23, 2010 #9

    Dick

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    It makes sense, but -1 isn't in S={0,1,2,3,4,5,6}. If there is an inverse, you need it to be a member of S.
     
  11. Sep 23, 2010 #10
    so there is no inverse since it does not exist in the S!
     
  12. Sep 23, 2010 #11

    Dick

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    Exactly.
     
  13. Sep 23, 2010 #12
    Thank you soooo much for your help and time!
     
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