JSH: Operator ambiguity, Escultura

From: James Harris (jstevh_at_msn.com)
Date: 11/27/04 

Date: 27 Nov 2004 13:59:51 -0800

I would like to pull out and highlight something interesting that E.
E. Escultura posted a few days ago, which I'd guess he's probably
talked about many times before, but I just noticed it and think it's
neat.

First some more preamble as *by convention* as has been noted when I
brought up the subject of operator ambiguity before, sqrt(x) is taken
to be positive.

So, by the convention, sqrt(4) = 2, and that's good as, -2(-2) = 4, so
if you say that sqrt(4) = 2 and sqrt(4) = -2, then 2 = -2, and 4 = 0,
which is not good.

Naively then, you may believe that you can just say, take the positive
of the square root but as Escultura showed, that doesn't work:

i = sqrt(-1) = sqrt(1/-1) = 1/i, giving -1 = 1. Contradiction.

You see, the ambiguity in the square root operator still remains,
despite the convention.

It doesn't work to just try and always take the positive as
Escultura's example shows so clearly.

Who has the resolution? I'm curious as to whether or not any of you
think you can answer.

James Harris

Relevant Pages

  • Re: Operator ambiguity, Escultura
    ... And then proclaiming that you have taken the positive square root. ... > brought up the subject of operator ambiguity before, ... > You see, the ambiguity in the square root operator still remains, ...
    (sci.math)
  • Re: JSH: Operator ambiguity, Escultura
    ... >You see, the ambiguity in the square root operator still remains, ... be under the impression that there is such a convention - there ... You also seem to be under the impression that i is positive, ... There's no contradiction to be resolved, ...
    (sci.math)
  • Re: JSH: Operator ambiguity, Escultura
    ... >> I would like to pull out and highlight something interesting that E. ... that the result of using the square root operator is two solutions. ... That's the operator ambiguity. ...
    (sci.math)
  • Re: how can I return nothing?
    ... If the square root function is defined simply as the number (or a ... I *think* there's also a mathematical convention for choosing the ... branches of mathematics, ... C defines a csqrtfunction that yields the complex square root of a ...
    (comp.lang.c)
  • Re: Why is this evaluation is not giving me the same solution
    ... Roger Stafford wrote: ... > Hello Koang, ... > remove the i^2 factor from inside the square root. ... Furthermore any other convention would be ...
    (comp.soft-sys.matlab)