I don?t know why I jump in to say anything on this, but a function can have
only one value. If it has more than one it is not a function, by definition
of mathematical functions. So sqrt(16)=4, not 4 and ?4 too.
So sqrt(-16) = 4*%i
I take the positive imaginary axis as the preferred answer for completely
arbitrary reasons. You know what positive imaginary means right? The part
of the imaginary axis ABOVE the real axis. I say it thus because I like it
better.
R
From: Richard Fateman
Sent: Friday, February 11, 2011 2:51 PM
To: Gary Pajer ; Maxima - list
Subject: Re: [Maxima] sqrt(x)*sqrt(x)
On 2/11/2011 10:26 AM, Gary Pajer wrote:
On Fri, Feb 11, 2011 at 10:10 AM, Richard Fateman
<fateman at eecs.berkeley.edu> wrote:
...
It seems hopeless to point out that x>0 does not mean that sqrt(x)>0,
mathematically.
There are 2 square roots. For example sqrt(16) is {-4, 4}, even though
16>0.
Perhaps that is true maxima-tically.
No, there are 2 square roots of 16, mathematically. Maxima chooses one of
them, 4,
and thus it is not true maxima-tically that there are 2 roots.
And perhaps 16 has two real roots.
There is nothing "perhaps" about it, unless you do not believe in negative
numbers.
S^2-16=0 defines the value(s) for S, corresponding to the square root of
16.
By some obscure theorem, the so-called "fundamental theorem of algebra"
there are 2 roots.
But as a mathematical *function* sqrt(16) = +4.
Nope. You mean "as a program written by one or more people, the conjunction
of
circumstances leads the Maxima system to return 4 when you type sqrt(16)."
Your
statement probably misuses at least one technical term, and maybe three.
"mathematical" "function" and maybe "sqrt".
The computer programming term "function" in common usage does not correspond
really to
the mathematical concept "function" except superficially.
Why am I bothering to comment on this?
Because failing to make such distinctions leads to
subtle but very bad consequences, even though it may seem harmless enough
for the
moment.
RJF
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