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sasogeek

what's the easiest way to determine whether the binary operation * is associative, if * is defined by \(x*y=\frac{x+y}{1+xy} \)

  • 2 years ago
  • 2 years ago

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  1. NotSObright
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    Define associativity

    • 2 years ago
  2. sasogeek
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    x*(y*z)=(x*y)*z ... if it's associative, then the right hand side should be equal to the left hand side

    • 2 years ago
  3. NotSObright
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    It is associative i did it by verifying LHS=RHS Although intuition pointed it right away

    • 2 years ago
  4. sasogeek
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    well is that the easiest way...? i was thinking maybe there's a faster method

    • 2 years ago
  5. Mr.Math
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    It clearly follows from the associativity of addition and multiplication.

    • 2 years ago
  6. sasogeek
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    what do u mean by that?

    • 2 years ago
  7. Mr.Math
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    I mean \((x*y)*z=\frac{(x+y)+z}{1+(xy)z}=\frac{x+(y+z)}{1+x(yz)}=x*(y*z).\)

    • 2 years ago
  8. sasogeek
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    ohhh okay, well i was doing some weird workings but the answer was quite obvious right from the beginning :) thanks

    • 2 years ago
  9. Mr.Math
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    You're welcome.

    • 2 years ago
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