SOLUTION: Hi i'm stuck on the following question:
"For the set of positive rational numbers, show that division as the operation of combination is not associative. For this set is there a
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Question 716179: Hi i'm stuck on the following question:
"For the set of positive rational numbers, show that division as the operation of combination is not associative. For this set is there any operation that is associative?"
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Given a set of positive integers 
, consider the combination:
\ \div\ \frac{u}{v}\ =\ \frac{ps}{qr}\ \div\ \frac{u}{v}\ =\ \frac{psv}{qru})
and consider:
\ =\ \frac{p}{q}\ \div\ \frac{rv}{su}\ =\ \frac{psu}{qrv}\ \not\equiv\ \frac{psv}{qru})
In general, subtraction and division are neither associative nor commutative over the Real numbers. Addition and Multiplication are both associative and commutative over all Real numbers. The set of positive rational numbers is a subset of the Reals.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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