Students: Find out why Cauchy's derivative definition is flawed.

[John Gabriel]

Five reasons:

https://www.youtube.com/watch?v=OT0ffnwMf7o

[Dan Christensen]

JG's New "Calclueless" is a dead end. It is a complete waste of time. His wonky definition of a derivative blows up even for such simple functions as y=x and y=x^3.


Dan

[John Gabriel]

On Monday, 30 January 2017 20:26:53 UTC-8, Dan Christensen wrote:
> JG's New "Calclueless" is a dead end. It is a complete waste of time. His wonky definition of a derivative blows up even for such simple functions as y=x and y=x^3.
>
>
> Dan

Hey Crank,
Jan Burse on vacation, so you are standing in for him? Chuckle.

Eat shit and die you lying bastard.

[Ross A. Finlayson]

Begone, McSpam.

That malvertising craptevision is no substitute
for a well-put-together usual development of the
Fundamental Theorem(s) of Calculus with their
usual general purpose support of real analysis,
and, that malvertising craptevision is both off-
topic and inane to "sci.math", a neat and usual
public resource that finds itself spammed with
malvertising craptevision.

Arguments otherwise as about philosophical aspects
of background, foundations, methods, and so on in
mathematics are of course anyone's to detail to
the extent they see fit, but hit-piece shit-shows
(for example, from the troll-bot crank) are not.

The troll-bot's "definition of a derivative" is
the same as rise/run, it emits "assume a tangent
line, write an equation as rise/run" then obfuscates
that with a limit as to compute rise/run of the
tangent line. That's not the derivative, it's
the tangent line's rise/run. (Crossing or non-
crossing it's the tangent line.) The troll-bot's
"MVT" isn't an MVT either, it just computes rise/run
with an obfuscating limit and says "that was the mean
value", which in no way establishes an MVT as
about the IVT about the Fund. Thm(S). of Calc.


Begone, foul McSpam, begone.

[John Gabriel]

On Monday, 30 January 2017 21:04:28 UTC-8, Ross A. Finlayson wrote:

> Gabriel's proof of the MVT is the first ever constructive proof

Correct. I don't have my own mvt and don't know where you got that idea? Oh wait, you are a moron. Sigh.

> it just computes rise/run of a tangent line

Exactly.

[Dan Christensen]

On Monday, January 30, 2017 at 11:45:28 PM UTC-5, John Gabriel wrote:
> On Monday, 30 January 2017 20:26:53 UTC-8, Dan Christensen wrote:
> > JG's New "Calclueless" is a dead end. It is a complete waste of time. His wonky definition of a derivative blows up even for such simple functions as y=x and y=x^3.
> >
> >
> > Dan
>

> Hey...

Why don't you tell the boys and girls why you are unable obtain the derivative of even a function as simple y=x in your New "Calclueless." And why you don't believe in zero, negative numbers, empty sets, pi or the square root of 2.

What moron!


Dan

[Ross A. Finlayson]

Besides its arsenal of threats,
now the troll-bot misattributed.

The troll-bot reads off the tangent line,
(that it's provided as an input to a
simple routine), in contrast, the Cauchy's
(quite standard) derivative computes the
formula for the tangent line.

Begone, McSpam, it's not just your wares
are counterfeit, they're not genuine.

They're not conscientious, not _sincere_.

This is sci.math, there's right and wrong
here, and right is right and wrong is wrong.

[John Gabriel]

On Monday, 30 January 2017 21:36:40 UTC-8, Ross A. Finlayson wrote:
> On Monday, January 30, 2017 at 9:14:07 PM UTC-8, John Gabriel wrote:
> > On Monday, 30 January 2017 21:04:28 UTC-8, Ross A. Finlayson wrote:
> >
> > > Gabriel's proof of the MVT is the first ever constructive proof
> >
> > Correct. I don't have my own mvt and don't know where you got that idea? Oh wait, you are a moron. Sigh.
> >
> > > it just computes rise/run of a tangent line
> >
> > Exactly.
>
> Besides its arsenal of threats,
> now the troll-bot misattributed.
>
> The troll-bot reads off the tangent line,
> (that it's provided as an input to a
> simple routine), in contrast, the Cauchy's
> (quite standard) derivative computes the
> formula for the tangent line.

It does no such thing. It tries to compute the slope but ALWAYS FAILS.

In fact, my video shows that the limit L is required by invalid arithmetic to be fed into the Weierstrass verifinition.

The 5 top reasons why the mainstream definition of the derivative is flawed:

(a) It requires limit theory. In order for limit theory to work, there must be a valid construction of real number in place. There isn't. Neither Dedekind Cuts nor equivalent Cauchy Sequences of rationals are valid constructions of real numbers.

(b) An invalid method involving division by 0 is required to find the limit L = f'(c).

(c) The limit definition is circular since it requires one already know the derivative:

Given any e>0 and d>0, both real numbers, then whenever

0<|x-c|<d => | [f(c+h)-f(c)]/h - L|<e

it follows that f'(c) = L. Thus, f'(c) is used in its own definition. This definition is more of a 'verifinition' because one can use it to show that L is the limit, but not without first finding L, that is, L=f'(c). See (b).

(d) For any straight line, the value of e and d are irrelevant and consequently, so is the definition given in (c).

(e) It gives rise to a contradiction in the meaning of tangent line.

---------------------------------------------------------------------------------------------------------------------

Even in terms of FO logic, the definition is irrelevant wrt straight lines.

Given e,d both in R and both greater than 0, then

whenever 0<|x-c|<d implies | { f(c+h)-f(c) } / h - L |<e

and L = f'(c).

In terms of straight lines:

0<|x-c|<d implies | 0 |<e

The relationship between d and e is equality in the case of straight lines, that is, d = e. Since |0|<e can never be false, the second and fourth rows of the imply truth table do not represent the predicate logic where straight lines are concerned.

Imply Truth Table:

T T T
T F F
F T T
F F T

The New Calculus does this correctly every time with the secant theorem.

<troll excrement>

[John Gabriel]

On Monday, 30 January 2017 19:58:24 UTC-8, John Gabriel wrote:
> Five reasons:
>
> https://www.youtube.com/watch?v=OT0ffnwMf7o

If you watch no other video, watch this one. Click on FULL SCREEN so you can read the text easily.

[Dan Christensen]

On Tuesday, January 31, 2017 at 3:39:28 PM UTC-5, John Gabriel wrote:
> On Monday, 30 January 2017 21:36:40 UTC-8, Ross A. Finlayson wrote:
> > On Monday, January 30, 2017 at 9:14:07 PM UTC-8, John Gabriel wrote:
> > > On Monday, 30 January 2017 21:04:28 UTC-8, Ross A. Finlayson wrote:
> > >
> > > > Gabriel's proof of the MVT is the first ever constructive proof
> > >
> > > Correct. I don't have my own mvt and don't know where you got that idea? Oh wait, you are a moron. Sigh.
> > >
> > > > it just computes rise/run of a tangent line
> > >
> > > Exactly.
> >
> > Besides its arsenal of threats,
> > now the troll-bot misattributed.
> >
> > The troll-bot reads off the tangent line,
> > (that it's provided as an input to a
> > simple routine), in contrast, the Cauchy's
> > (quite standard) derivative computes the
> > formula for the tangent line.
>
> It does no such thing. It tries to compute the slope but ALWAYS FAILS.
>

Wrong again, Troll Boy. In your New "Calclueless," you are unable to obtain the derivative of y=x and of y=x^3. Refusing to rework an obviously flawed definition, you decree instead that they are henceforth to be considered "undefined." What a moron!


Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[Ross A. Finlayson]

A derivative isn't just a slope of a curve,
it's a slope of the function of a curve,
and that's determined for a wide range of
curves, and indeed is the instantaneous
rate of change for the limit of rise/run
as run goes to zero, not that run = 0,
but the limit rise/run as run -> 0. The
limit has to be defined for the function
of the curve for that to exist, and it does
for the continuous curves as are thus called
"differentiable". (That may be an existence
result besides a proviso.) Then, the chain
rule, power rule, derivatives of trigonometry,
the exponential, and other computations of
derivatives are applications of that.

None of the troll-bot's objections apply
and delta-epsilonics beats them quite thoroughly.
Then, besides, the troll-bot just depends on
having a tangent line being provided already,
with no computational ability, it's ungenuine
besides counterfeit.

Kinks (as not of continuous curves as smooth)
like f' |x| at 0 are just treated as the
removable discontinuities, with otherwise
usually the existence from the right and
left, and even possibly the assignment of
the value as the mean (as removable). As
gradient besides slope in models of force,
like "the ski jump", it's familiar with
those who've completed a few years course
in fundamentals and applications of real
analysis that models of motion are pretty
much smooth.

Fourier and Taylor refer to being able to
rewrite periodic and continuous functions
as sums (series) of elementary orthogonal
and derivative functions. (These are then
very widely used in methods and applications.)

"The reverse process is called _antidifferentiation_."
-- https://en.wikipedia.org/wiki/Derivative

Our integral calculus has integrals besides derivatives.

Continuity, as of the existence of a continuous
domain, and then continuous functions as continuous
transforms, I have here that Cantor proves that
the line is drawn to well-order the reals and
thus that's the constructive establishment of
continuity, as I've so noted here in terms of
"Foundations of Continuity".

[John Gabriel]

On Tuesday, 31 January 2017 14:51:58 UTC-8, Ross A. Finlayson wrote:

> A derivative isn't just a slope of a curve,

No curves have any slope you moron. The slope of a curve is defined to be the slope of the tangent line at a given point. You ignorant fool.

> it's a slope of the function of a curve,
> and that's determined for a wide range of
> curves, and indeed is the instantaneous
> rate of change for the limit of rise/run

Nothing changes dummy. Those tangent lines have remained unchanges forever.

<troll excrement dumped>

[Ross A. Finlayson]

The pestilent goon troll-bot,
has lost.

There's only adding to mathematics,
not taking away.

Hilbert's Infinite Museum doesn't need a
guard, except perhaps as defenders of the
orthodoxy might look to prevent vandalism
of the exhibits, there's always a right
and wrong and right is right and wrong is
wrong. Exhibits might move about but they're
always available to all, via what various
circuitry there may be.

Curves have gradients in accordance with
the coordinate systems of functions as
so define them.

Thread's dead.

The troll-bot's thread is dead.

If you wanted to be interesting, there are
many interesting fields in mathematics, and
they are all highly interrelated. Foundations
is a matter of particular interest to many,
most, or all. Since antiquity, enshrined
reason has been about the faculties of logic
and mathematics as the higher order in the
reasoning, then onward beyond applications
to the mathematical sciences and otherwise
to its tremendous and ubiquitous utility,
and in all matters of reckoning. Foundations
is of particular interest to many, in part
for the consideration of the best in definition,
and in part for the consideration of the
resolution in paradox, then particularly,
for both the best in definition and the
resolution of paradox, toward the constant,
consistent, complete, then concrete in the
foundations. This was among the goals that
Hilbert championed. A century later, modern
mathematics is well established as platform,
and the trade-offs of consistency and completeness
are well-explored, and there are attempts to
find the resolution of the yet remaining paradoxes
and further redefinition, where the best definition
is the least.

Then, this isn't trying to close off some deemed
incompatible wing of the H.I.M., there's always
another route because that's mathematics. What
you need is to find the door.

So, that said, and metaphor fails, except the
strong metonymy, there have been trolls since
Ancient Greece, and there will be trolls in
the later 21'st century, don't be them and
don't feed them.

And don't be accepting un-acceptable, fraudulent,
un-genuine, counterfeit modern craps on toilet
paper, even if they're signed.

That's not art, and it's not science,
and it's not mathematics.