Fw: can someone answer my question?

[kkollins at pop3.concentric.net]

Walter Eric Johnson wrote:

> kkollins at pop3.concentric.net wrote:
> : Walter Eric Johnson wrote:
> :
> : > How many solutions does cos(x)=0 have?
> :
> : One talks about "solving" a function for its x-axis intersections, but "zeroes" of a function are
> : not "Solutions" to the function... they are Solutions to a =specific subset= of a function's
> : domain, determined by both the function's general Solvability =and= the value of the independent
> : variable... in the above, "x"... the =Solution" to a function is the function, itself, Proven for
> : all values of its independent variable(s)... there's always just one of these. Proven functions are
> : numerical-domain "maps"... given such a function, one can find one's way within the numerical
> : domain with respect to which the function has been Proven... just as one can use a regular
> : topographical map to find one's way
> :
> : [...]
>
> Are you really sure that you're an expert in Math?  I mean this is no
> more than college algebra.  And to top it off, your explanation makes
> little or no mathematical sense at all.

I stand on what I posted.

> Just in case you were gone that day in your days before becoming an
> expert in Math, I'll attempt to explain it:
>
> If you have an equation that you wish to solve, for example, g(x)=h(x),
> you are trying to find those values of x for which g(x)=h(x).  Those
> values of x for which the expression is true are called the "solutions".

They are "answers" within a limited numerical domain, albeit, part of the Solution... calling them
"solutions" doesn't embue them with the Generalized Quality of Solution... look back in "WEJ's" posts...
"Mathematicians construct Proofs", or something like that is what "WEJ" posted.

> So if g(x)=h(x), you can define a function f(x)=g(x)-h(x).  Then those
> values of x for which g(x)=h(x) also result in f(x)=0.  Thus, the solutions
> of the equation g(x)=h(x) are the values of x for which f(x)=g(x)-h(x)=0.

There's only one Solution to any Equation... that which Maps its entire numerical-domain. It doesn't
matter what the books 'say"... all one has to do to Prove the Veracity of the One-Generalized-Solution
view is subject a piece-by-piece "problem-solver" to more individual instances of the Generalized
Solution than the piecemeal Calculator can Calculate in its piecemeal way... the calculator will "have a
fatal siezure", to quote one of "WEJ's" posts... and, in such, it's seen that Solution is Absent... it's
what the "N-P Completeness" folks go on and on about.

> In other words, when you are solving the equation g(x)=h(x), you are
> finding the zeros of the function f(x)=g(x)-h(x).

One zero does not a Solution make.

All zeroes do not a Solution make.

Solution exists in the Proof that a function's numeric domain has been completely Mapped... most of most
such numeric domains are mostly non-zero stuff... it's an exceedingly-Strange function that's just zeroes
("present" company excluded, of course).

> Now wasn't that easy?  And it didn't take any private buzzwords to
> explain, either.

It was "just" Wrong... filled with "definitions" beating themselves over the head... I made it clear in a
prior post to "WEJ" that I tend to only "bother" folks with stuff that's not yet in the books, Trusting
that if folks want to use what's already in the books, folks'll go to the books, find what they want, and
use it... when the demands on my "time" are as they are, why should I reiterate what's already in the
books? I could never do as good a job as the folks who've already written the books, could I? So why
reiterate what's already in the books? For me, such'd be Waste.

> : I stand on what I've posted... Clearly, there is a "Robot Responder", and just as Clearly, the
> : "goals" inherent in the Programming of that "Robot Responder are Inverted with respect to Truth. K.
> : P. Collins
> :
> : [to ALL: I =Apologize= that all of this is occurring in your Electronic Presence. K. P. Collins]
>
> Look at it this way, you were posting bunches of messages a day.  Now
> you're posting a whole lot less messages to have to weed through.  That's
> what I call improvement.

Thousands will Perish Be-Cause of the delay imposed by "WEJ". K. P. Collins