Re: A little lesson for sqrt(144) year olds.

From: Androcles (androc1es_at_nospamblueyonder.co.uk)
Date: 07/01/04 

Date: Thu, 01 Jul 2004 12:01:20 GMT

"Jesper Pedersen" <jesper@befunk.com> wrote in message
news:cc0hvk$uf8$1@news.net.uni-c.dk...
| "Androcles" <androc1es@nospamblueyonder.co.uk> wrote in message
| news:kwCEc.88$rd1.1081531@news-text.cableinet.net...
| <snip>
| > | You need to understand the fundamental difference between solving
x^2=2
| > for
| > | x
| >
| > I think the solution is -1.4142135623730950488016887242097.
| > Let's see.
| > -1.4142135623730950488016887242097 *
| > -1.4142135623730950488016887242097 = 2.
| > Yep, I'm right.
|
| Almost, but not quite right.
On a scale of right (1) to wrong (0), where is "not quite"? 0.5? 0.6? 0.9
maybe?

There are two solutions to the equation, yours
| is one of them.

Well done. How very perceptive of you.

I suspect that you know this, or at least I sincerely hope
| so.

So we agree. sqrt(2) has two solutions.
|
| > and applying the function sqrt(2). the sqrt is DEFINED as being
positive.
I see. Who by?
| > Is it?
| > if x = [-b +/- sqrt(b^2 - 4ac]/2a, is b always positive?
|
| What does that have to do with sqrt(x) being positive by definition?

Well, you seem to be following some rule I'm not aware of.
I'm trying to figure out what it is.
If -2 is a sqrt of 4, then sqrt(4) * sqrt(4)= 4
and also -sqrt(4) * -sqr(4) = 4.
What's nearly wrong with that?

| sqrt(b^2-4ac) is always positive, but you may choose b to be whatever
suits
| your fancy. Why do you even choose to write the equation the way you do?

To emphasize and describe algebraically there are two roots, of course. Its
shorthand.
What's nearly wrong with that?

| If
| you believe sqrt(x) to be both positive and negative, why the need for the
| +/- in front of it?

I never said it was both, I said there were two solutions.

| > | Otherwise how would equalities such as sin(Pi/4) = sqrt(2)/2 make any
| > sense
| > | at all? Surely you wouldn't claim that sin is dual-valued?
| > That rather depends on whether you use (x, iy) or (x,y), doesn't it?
| > Androcles.
|
| I fail to see how sin(Pi/4) can ever be anything other than sqrt(2)/2 > 0.
| And let's just stick to x belonging to R shall we?
Why? What's nearly wrong with z = {x + iy} ?

| Would you at least agree
| then, that sin(x) is not dual-valued?

Would you at least agree tht bight green flying elephants lay eggs, Or am I
being irrelevant?

| Or am I wasting time on a troll?

Ah, the first insinuation that someone you disagree with must have some evil
motive in mind, although there are two solutions to sqrt(), one of them
negative, and sqrt() is defined as positive. Next you'll begin snipping and
ignoring and name calling, just like the rest of the trolls that lurk around
here.

Androcles.

|
| / Jesper P
|
|

Relevant Pages

  • Re: A little lesson for sqrt(144) year olds.
    ... | You simply multiply the negative root by the positive one. ... |>| Or am I wasting time on a troll? ... and sqrt() is defined as positive. ...
    (sci.math)
  • Re: A little lesson for sqrt(144) year olds.
    ... | You simply multiply the negative root by the positive one. ... |>| Or am I wasting time on a troll? ... and sqrt() is defined as positive. ...
    (sci.physics)
  • Re: A little lesson for sqrt(144) year olds.
    ... | You simply multiply the negative root by the positive one. ... |>| Or am I wasting time on a troll? ... and sqrt() is defined as positive. ...
    (sci.physics.relativity)
  • Re: A little lesson for sqrt(144) year olds.
    ... | "Androcles" wrote in message ... |> | You need to understand the fundamental difference between solving ... | Or am I wasting time on a troll? ... motive in mind, although there are two solutions to sqrt(), one of them ...
    (sci.math)
  • Re: A little lesson for sqrt(144) year olds.
    ... | "Androcles" wrote in message ... |> | You need to understand the fundamental difference between solving ... | Or am I wasting time on a troll? ... motive in mind, although there are two solutions to sqrt(), one of them ...
    (sci.physics)