Question 716179
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Given a set of positive integers *[tex \LARGE \mathbb{Z}_\alpha\ =\ \{p,\, q,\, r,\, s,\, u,\, v\}], consider the combination:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{p}{q}\ \div\ \frac{r}{s}\right)\ \div\ \frac{u}{v}\ =\ \frac{ps}{qr}\ \div\ \frac{u}{v}\ =\ \frac{psv}{qru}]


and consider:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{p}{q}\ \div\ \left(\frac{r}{s}\ \div\ \frac{u}{v}\right)\ =\ \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
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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