sasogeek
  • sasogeek
what's the easiest way to determine whether the binary operation * is associative, if * is defined by \(x*y=\frac{x+y}{1+xy} \)
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Define associativity
sasogeek
  • sasogeek
x*(y*z)=(x*y)*z ... if it's associative, then the right hand side should be equal to the left hand side
anonymous
  • anonymous
It is associative i did it by verifying LHS=RHS Although intuition pointed it right away

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sasogeek
  • sasogeek
well is that the easiest way...? i was thinking maybe there's a faster method
Mr.Math
  • Mr.Math
It clearly follows from the associativity of addition and multiplication.
sasogeek
  • sasogeek
what do u mean by that?
Mr.Math
  • Mr.Math
I mean \((x*y)*z=\frac{(x+y)+z}{1+(xy)z}=\frac{x+(y+z)}{1+x(yz)}=x*(y*z).\)
sasogeek
  • sasogeek
ohhh okay, well i was doing some weird workings but the answer was quite obvious right from the beginning :) thanks
Mr.Math
  • Mr.Math
You're welcome.

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