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Unary minus precedence preference
07-23-2014, 01:45 PM
Post: #14
RE: Unary minus precedence preference
(07-23-2014 02:36 AM)John R Wrote:  
(07-22-2014 07:56 AM)Thomas Radtke Wrote:  There is no proof. It's a convention.

That said, it's a very useful convention, symbolically speaking. It seems that if one chose the opposite convention, making \(-2^2=4\), then consistency would demand that \(-x^2=x^2\) for all \(x\). Algebraic expressions would then be fraught with many more parentheses than we are used to, with \(-(x^2)\) being the expression required to denote the negation of \(x^2\), for instance.

Finally, a well funded response. So one good reason to choose -2^2=-4 is to avoid unnecessary parenthesis and the ambiguity of:
x-x^2 producing a different result from -x^2+x.
Notice the first minus is a subtraction, while the second minus becomes a unary minus just by commutativity, so they are two different operators but the expressions are mathematically equivalent and should give the same result.
This alone is reason enough to discard the other option as "incorrect", as a CAS cannot give 2 different results just for swapping terms in the expression.
Thank, John, your argument is enough to convince me that there should NEVER be an option to do -2^2=4, because when used in more complex expressions it has disastrous consequences.

Claudio
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RE: Unary minus precedence preference - Claudio L. - 07-23-2014 01:45 PM



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