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Topic: Please remind me why -3^2 = -9
Replies: 26   Last Post: Nov 18, 2012 7:51 PM

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 Phil Mahler Posts: 126 Registered: 12/6/04
Re: Please remind me why -3^2 = -9
Posted: Oct 18, 2012 8:33 PM
 att1.html (2.6 K)

This is a good discussion on such a seemingly simple expression.

I don¹t see two operations in ­3^2. I see a number, -3, being squared. ...
Or, I would see that, if I hadn¹t been told otherwise. Just like 3^2 means 3
being squared.

As someone noted the dash is used for multiple meanings, to indicate we want
the additive inverse of say 3, or to say we want to subtract 3 from 10, 10 ­
3, which, using the most common definition, is meaningless without knowing
that a ­ b means a + (-b), so the dash really does mean we want an opposite
of a value, and is not, in fact, an operation.

I sometimes see students who were taught to use a smaller elevated dash to
indicate the negative of a number, so 10 - (-3) would be written 10 - -3,
with the second dash small, elevated and closer to the 3. That might
disambiguate ­3^2, depending on which symbol is used. The smaller one means
you are squaring a ­3, the larger symbol by the definition above must mean 0
­ 3^2 (a = 0) and so PEMDAS actually helps there.

I also don¹t see the problem with PEMDAS, since it is, as far as I can tell,
also arbitrary, and established by custom and not axioms.
In 3 + 5 x 2, I don¹t see an axiom that would tell me what to do first. So I
wouldn¹t know how to explain it without noting the custom.

Of course maybe I¹m displaying an ignorance of the properties of a field or
something.

Phil

On 10/18/12 1:26 PM, "Paul Hertzel" <hertzpau@niacc.edu> wrote:

> Although I agree with Jack Rotman about the damage inflicted by PEMDAS, I'm
> not sure
>
> . . ."the expression ³-3^2² deals with the order of operations"
>
> gets to the heart of the problem. The reason is, in this case, the little
> horizontal bar in front of the 3 could be a part of the number's name. So
> "-3^2" is not two operations, just like "43^2" is not two operations. In the
> latter, the 4 is part of the number's name, it is not a multiplier.
>
> This is the problem, in this case, and so I think Guy Brandenburg is right.
> Writing -3^2 is just asking for trouble.

Date Subject Author
10/18/12 Phil Mahler
10/18/12 John Peterson
10/18/12 Guy Brandenburg
10/18/12 Wayne Mackey
10/18/12 Phil Mahler
10/18/12 RotmanJ
10/18/12 Paul Hertzel
10/18/12 Phil Mahler
10/18/12 Clyde Greeno
10/19/12 Clyde Greeno
10/19/12 Alain Schremmer
10/19/12 Wayne Mackey
10/19/12 Alain Schremmer
10/19/12 Clyde Greeno
10/19/12 Alain Schremmer
10/21/12 Wayne Mackey
11/14/12 Beth Hentges
11/15/12 Clyde Greeno
11/16/12 Alain Schremmer
10/18/12 Collinge, Peter (Mathematics)
10/18/12 Guy Brandenburg
10/18/12 Phil Mahler
10/18/12 Alain Schremmer
11/18/12 EddieC
11/18/12 Matthews, George
11/18/12 Phil Mahler
11/18/12 Alain Schremmer