Re: 0^0


<mensanator@xxxxxxx> wrote in message
news:1125878767.406100.158390@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|
| Androcles wrote:
| > <mensanator@xxxxxxx> wrote in message
| > news:1125868903.235204.326240@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > |
| > | Androcles wrote:
| > | > <mensanator@xxxxxxx> wrote in message
| > | > news:1125866361.989676.89780@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > | > |
| > | > | Androcles wrote:
| > | > | > "David W. Cantrell" <DWCantrell@xxxxxxxxxxx> wrote in
message
| > | > | > news:20050904150828.396$5h@xxxxxxxxxxxxxxxxx
| > | > | > | FunkyRes <mpeters@xxxxxxx> wrote:
| > | > | > | [snip]
| > | > | > | > Nevermind - after reading this thread, defining it as 1
| > makes
| > | > | > perfect
| > | > | > | > sense, it just does not have a limit approaching it from
the
| > | > left in
| > | > | > the
| > | > | > | > particular case I was remembering (from the right, the
limit
| > was
| > | > in
| > | > | > fact
| > | > | > | > 1)
| > | > | > | >
| > | > | > | > ax^2+bx^1+cx^0
| > | > | > | >
| > | > | > | > only makes sense if x^0 is defined as 1 - and I don't
think
| > | > there is
| > | > | > a
| > | > | > | > case (that I can think of) where a function could be
| > expressed
| > | > as
| > | > | > 0^0
| > | > | > | > where it wouldn't have a limit of 1 from one side or the
| > other,
| > | > so
| > | > | > | > defining it as 1 doesn't break anything.
| > | > | > |
| > | > | > | There are such cases, however. A simple example is 0^|x|.
As x
| > | > | > approaches
| > | > | > | 0 from either side, the limit is obviously 0. If that
example
| > | > seems
| > | > | > too
| > | > | > | trivial:
| > | > | > |
| > | > | > | Let f(x) = |x|^log(c) for any desired positive real c and
g(x)
| > =
| > | > | > 1/log|x|.
| > | > | > | As x approaches 0 from either side, f(x) and g(x) both
| > approach 0,
| > | > | > while
| > | > | > | f(x)^g(x) approaches c.
| > | > | > |
| > | > | > | But the important point is that, regardless of the
existence
| > of
| > | > such
| > | > | > cases,
| > | > | > | having 0^0 = 1 still "doesn't break anything".
| > | > | > |
| > | > | > | David
| > | > | >
| > | > | > Of course it will break something, you haven't seen the
| > application
| > | > | > where the robot arm takes off someone's head yet.
| > | > |
| > | > | Why would you program a robot with invalid mathematics?
| > | >
| > | > I wouldn't, but I've seen it done. Don't hire David Cantrell.
| > | >
| > | > | A properly written program can't make that mistake.
| > | >
| > | > The key word is "properly". Cantrell thinks x^x will resolve
| > | > to 1 when x = 0 comes up from transducer because the
| > | > signal line was cut by a fork truck running over it and the
| > | > arm will take off someone's head instead of halting on an
| > | > exception *properly* handled by an exception handler.
| > |
| > | So what happens when the transducer legitimately outputs a 0?
| > | If 0 is an invalid output, shouldn't that be tested BEFORE
| > | you plug it into an equation and cross your fingers and hope
| > | it generates an exception? Frankly, I'm surprised you even allow
| > | your receivers to see a 0 signal when a cable is cut. Sounds
| > | like sloppy engineering to me.
| >
| > There you have it. It's an exception if you do, and managed
| > properly by an exception handler. Cantrell and his ilk want
| > the exception to be always handled one way only.
|
| Except that 0^0 doesn't raise an exception.
|
| > You are advocating redundant code in the form
| >
| > Application programmers code:
| > If x = 0 then goto exception
| > else
| > {
| > (operating system code)
| > if y/x = 0/0 then 1 and carry on computing,
| > let robot kill someone.
| > }
| > instead of using only the operating system's
| > if y/x = 0/0 goto exception.
| >
| > All this is about is a whim that someone thinks
| > it's smart to let 0/0 = 1 when it is really undefined.
|
| Nobody said that. They said 0^0 = 1.

Nobody said 2+2 = 4, they said 2*2 = 4 and someone else
said 2^2 = 4. Your willful and deliberate attempts at stupidity
have been successful. You can stay out of the real world too.



|
| > That kind of smart will kill, the feds will be all over
| > the code AFTER the event, the company will be sued
| > for millions and the programmer fired at best or jailed as well.
| > Best to fire him before it happens, that does him a favour
| > and everyone else, but first I'll try to correct him.
| > I was paid well as a Quality Assurance Manager and
| > I knew my job.
|
| But apparently you didn't know it very well.

I think I knew it well enough to tell you to *** off.
*plonk*

Androcles.



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