Not just all "yahoo answers" but even excel says that -2^2=4 whereas this is totally wrong, as all math books will agree, since negation is taken as a multiplication, and exponentiation is done before multiplication. Will mathematical notation change due to this widespread ignorance? It seems that the internet is the culprit.for this "Idiocracy" come true.
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Unary minus is usually given lower precedence than exponentiation, but as you found out this is not always the case. According to Wikipedia, Microsoft Excel and also the programming language bc give unary minus higher precedence
http://en.wikipedia.org/wiki/Order_of_op…
As someone with hands in both mathematics and programming, I can say Excel and bc are atypical in this regard. For example, in Haskell -2^2 evaluates to -4, and in Perl and Python -2**2 evaluates to -4. In fact, until about a year ago, I didn't know that the convention used in Excel existed.
Different authors/fields use different notations/conventions, it's as simple as that. In general, such differences don't cause significant communication problems except for those who are not familiar with the territory (read: newbies!). It can be an inconvenience, but it's hard to eliminate because the conventions are embedded in the literature/language.
Specialists understand that different conventions exist, and they choose a convention appropriate in their field and communicate accordingly. When in doubt, notation can be defined before it is used.
I disagree with your claim that having different notations makes mathematics inexact. It's analogous to one author writing in English and another in French. Sure, it might cause problems if you can't read French, but that doesn't invalidate anything. And in reality the differences in notation are not nearly as dramatic as the differences between English and French.
http://en.wikipedia.org/wiki/Order_of_op…
As someone with hands in both mathematics and programming, I can say Excel and bc are atypical in this regard. For example, in Haskell -2^2 evaluates to -4, and in Perl and Python -2**2 evaluates to -4. In fact, until about a year ago, I didn't know that the convention used in Excel existed.
Different authors/fields use different notations/conventions, it's as simple as that. In general, such differences don't cause significant communication problems except for those who are not familiar with the territory (read: newbies!). It can be an inconvenience, but it's hard to eliminate because the conventions are embedded in the literature/language.
Specialists understand that different conventions exist, and they choose a convention appropriate in their field and communicate accordingly. When in doubt, notation can be defined before it is used.
I disagree with your claim that having different notations makes mathematics inexact. It's analogous to one author writing in English and another in French. Sure, it might cause problems if you can't read French, but that doesn't invalidate anything. And in reality the differences in notation are not nearly as dramatic as the differences between English and French.
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You are incorrect in thinking PEDMAS has anything to do with this. If a number is negative, well then it is negative, it isn't a function that you do after parenthesis, exponents, mult/divide.....
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keywords: quot,negative,squaring,numbers,about,Why,ignorance,in,as,such,Why such ignorance about squaring negative numbers, as in "-2^2"