Re: A little lesson for sqrt(144) year olds.
From: Randy Poe (poespam-trap_at_yahoo.com)
Date: 06/30/04
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Date: 30 Jun 2004 13:43:47 -0700
"Androcles" <androc1es@nospamblueyonder.co.uk> wrote in message news:<gE_Dc.5331$g23.56853778@news-text.cableinet.net>...
> "Randy Poe" <poespam-trap@yahoo.com> wrote in message
> news:df76407e.0406280228.1dd76ede@posting.google.com...
> | "Androcles" <androc1es@nospamblueyonder.co.uk> wrote in message
> news:<knPDc.4759$yy4.50343119@news-text.cableinet.net>...
> |
> | > Let's see now.
> | > 3 = x
> | > -3 = -x
> | > This way x is ALWAYS positive, right, Dinky?
> |
> | It is if x is 3, as you asserted on line 1.
> |
> | Do you have an example where 3 is negative?
> |
> | Do you think the second statement can be true for negative x?
> |
> | Randy
> Those were Dinky the Deranged's ideas, you had better ask him.
I agree that the first statement and the second one are
equivalent. I'm asking why YOU have a problem with the second
one, or the assertion that if x = 3, then x is always positive.
> He said
> Quote:
> "3 = sqrt(9)
> -3 = -sqrt(9)" -Dinky the Deranged.
> "This way sqrt is ALWAYS positive."-Dinky the Deranged.
> Unquote.
Yes. That's correct. The symbol "sqrt(9)", like your x,
stands for a positive quantity. If you want to refer to a
negative quantity with the same absolute value, you can
write a negative sign on both sides. Thus, -3 = -sqrt(9)
certainly follows from the definition of sqrt(9) as the
positive value whose square is 3.
Just as -3 = -x follows from the statement that 3 = x.
> I merely substituted x for sqrt(9).
OK. And why is it that you think -3 = -x is wrong when
you write 3 = x?
> Make sure you never write x = -3 because x is always positive,
No. Make sure that if you claim x = 3, you don't claim
x is simultaneously equal to -3.
"x" is not a symbol that has a sign convention in it. Nowhere
does Dirk or anyone else claim that the symbol "x" can only
be used for positive quantities.
On the other hand, the symbol "sqrt(x)" IS defined, by convention,
to stand for the non-negative root of y^2 - x. Since sqrt, unlike
x, has a sign-convention associated with it, then it is incorrect
to write "sqrt(9) = -3".
The thing on the left is >=0, the thing on the right is <0. They
can't be equal. There certainly is a negative root to y^2 - 9.
The symbol we use for that root is "-sqrt(9)".
> Dinky says so. You MUST write -x = -3.
You seem to have trouble with a really elementary concept here.
If we define sqrt(9) to be 3, then -sqrt(9) is -3.
If we define x to be 3, then -x is -3.
- Randy
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