Question 187446
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The commutative property only applies to addition and multiplication.


Commutative Property of Addition:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  a + b = b + a\ \forall\ a,\,b\,\in\,\R]


Commutative Property of Multiplication:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  ab = ba\ \forall\ a,\,b\,\in\,\R]


Of course, this causes us no problems whatsoever because, for those of us who understand the concepts of signed numbers and reciprocals, there is no such thing as subtraction and division.


Subtraction is actually addition of the additive inverse, in other words:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7 - 2]


Which operation is <i><b>not</b></i> commutative because:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7 - 2 \neq 2 - 7]


But the operation is really:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7 +(- 2)]


Which is commutative because:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7 +(- 2) = -2 + 7]


Likewise, division is simply multiplication by the reciprocal.


Division is not commutative:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4 \div 2 \neq 2 \div 4]


But


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4 \div 2 ]


is really:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4 \times \frac{1}{2}]


and this operation <i><b>is</b></i> commutative because:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4 \times \frac{1}{2} = \frac{1}{2} \times 4]






John
*[tex \LARGE e^{i\pi} + 1 = 0]
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