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I guess that when dealing with negative numbers we should use brackets to
ensure correct precedence.
Lionel Issen
lissen@xxxxxxxxxxxxxx
----- Original Message -----
From: "Glen Wallace" <gcwallace@xxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: Wednesday, September 19, 2001 7:44 PM
Subject: Re: Exponents and negative numbers
> Thanks for pointing that out, Walter. Interestingly, Quattro Pro says
> that -2^2 is -4, while Excel (as you say) computes -2^2 as +4.
>
> My first reaction was that you were squaring a negative number, but
> on looking at it again, the precedence of arithmetical operations says
> that exponents are always computed first. Excel is wrong.
>
>
>
> ----- Original Message -----
> From: "W Lake" <wlake@xxxxxxxxx>
> To: <metastock@xxxxxxxxxxxxx>
> Sent: Wednesday, September 19, 2001 8:08 PM
> Subject: Exponents and negative numbers
>
> > I have checked Mathematica, MathCAD and Derive. All three say
> > that -2^2 = -4, that -2^4 = -16 and that all of the data points from any
> > series, say out to -2^64 are on a negative power curve.
> >
> > There is no mention of using brackets or any special "input" techniques
to
> > handle negative numbers.
> >
> > Attached is an explanation of why -3^2 = -9 from a web site. If the
> > explanation is correct, then Excel (-2^2 = 4) is wrong and I need to
rethink
> > my usage.
> >
> > Can anyone add to or refute the logic given in the emails below.
> >
> > Walter
> >
> > =============================================
> >
> > Exponents and Negative numbers
> >
> > Date: 03/02/97 at 11:15:14
> > From: Anonymous
> > Subject: Exponents and negative numbers
> >
> > Dear Dr. Math,
> >
> > In different texts about this same question, I can find two different
> > answers. The solution to: (-3)squared = 9. But when -3 is squared
> > (without the brackets), one source may say 9 while another source
> > says -9.
> >
> > In context, the -3 squared used in sequence will always be -9; why
> > would the exponent apply to the negative sign unless it is enclosed
> > by a sign of grouping? In short, why wouldn't the answer to -3
> > squared, standing alone and without parenthesis or brackets, be -9?
> >
> > Thanks very much.
> >
> > Sincerely,
> > Marvin E. Crim
> >
> >
>
> --------------------------------------------------------------------------
--
> > ----
> >
> >
> > Date: 03/09/97 at 14:53:39
> > From: Doctor Ken
> > Subject: Re: exponents and negative numbers
> >
> > Hi Marvin -
> >
> > After a lengthy discussion among the Drs. Math to make sure we had our
> > facts straight, I think we have an answer for you.
> >
> > If you ever see the expression -3^2 evaluated as 9, that's incorrect.
> > The exponentiation is always done before the negation unless there are
> > parentheses there to indicate otherwise.
> >
> > However, there are some contexts in which it _looks_ like texts are
> > saying that -3^2 = 9, but a closer inspection will either reveal a
> > subtle interpretation or a misunderstanding. For instance, what is the
> > difference between the following statements:
> >
> > "If I take negative three and square it, I get nine."
> > "If I square negative three, I get nine."
> > "If I evaluate negative three squared, I get negative nine."
> > "If I take the opposite of three squared, I get negative nine."
> >
> > All of the above statements are correct. The reason some of them
> > end up with 9 as the answer and some end up with -9 is that some of
> > the statements have groupings implied in their phrasing. The first
> > two statements translate into algebraic notation as (-3)^2 = 9, the
> > third statement translates to -3^2 = -9, and the fourth statement
> > translates to -(3^2) = -9.
> >
> > So the confusion here is not really about mathematical notation, it's
> > about how to translate English into mathematical notation. Either
> > that, or your textbook is incorrect!
> >
> > I hope we've cleared up some confusion. The bottom line is that
> > -a^b is always evaluated as -(a^b).
> >
> > -Doctor Ken, The Math Forum
> > Check out our web site! http://forum.swarthmore.edu/dr.math/
>
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