On Monday, January 20, 2020 at 4:55:06 PM UTC-8, Ross A. Finlayson wrote:
> On Friday, January 17, 2020 at 7:43:33 PM UTC-8, Ross A. Finlayson wrote:
> > On Friday, January 17, 2020 at 5:43:18 PM UTC-8, Eram semper recta wrote:
> > > On Friday, 17 January 2020 16:36:19 UTC-5, konyberg wrote:
> > > > fredag 17. januar 2020 21.50.18 UTC+1 skrev Eram semper recta følgende:
> > > > > On Friday, 17 January 2020 15:06:10 UTC-5, konyberg wrote:
> > > > > > fredag 17. januar 2020 20.49.38 UTC+1 skrev Eram semper recta følgende:
> > > > > > > On Friday, 17 January 2020 14:15:33 UTC-5, konyberg wrote:
> > > > > > > > fredag 17. januar 2020 19.25.05 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > On Friday, January 17, 2020 at 11:06:52 AM UTC-5, konyberg wrote:
> > > > > > > > > > fredag 17. januar 2020 16.18.44 UTC+1 skrev konyberg følgende:
> > > > > > > > > > > fredag 17. januar 2020 15.20.12 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > > > > On Friday, 17 January 2020 09:16:33 UTC-5, konyberg wrote:
> > > > > > > > > > > > > onsdag 15. januar 2020 13.28.16 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > > > > > > On Wednesday, 15 January 2020 04:48:52 UTC-5, konyberg wrote:
> > > > > > > > > > > > > > > tirsdag 14. januar 2020 23.35.10 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > > > > > > > > On Tuesday, 14 January 2020 17:21:18 UTC-5, konyberg wrote:
> > > > > > > > > > > > > > > > > tirsdag 14. januar 2020 23.12.20 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > > > > > > > > > > On Tuesday, 14 January 2020 17:02:43 UTC-5, konyberg wrote:
> > > > > > > > > > > > > > > > > > > tirsdag 14. januar 2020 22.52.44 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > > > > > > > > > > > > On Tuesday, 14 January 2020 13:23:22 UTC-5, konyberg wrote:
> > > > > > > > > > > > > > > > > > > > > tirsdag 14. januar 2020 19.18.26 UTC+1 skrev Eram semper recta følgende:
> > > > > > > > > > > > > > > > > > > > > > On Tuesday, January 14, 2020 at 12:36:13 PM UTC-5, Ross A. Finlayson wrote:
> > > > > > > > > > > > > > > > > > > > > > > On Tuesday, January 14, 2020 at 4:46:34 AM UTC-8, Eram semper recta wrote:
> > > > > > > > > > > > > > > > > > > > > > > > On Tuesday, January 14, 2020 at 12:53:56 AM UTC-5, Ross A. Finlayson wrote:
> > > > > > > > > > > > > > > > > > > > > > > > > On Sunday, January 12, 2020 at 11:24:00 PM UTC-8, Zelos Malum wrote:
> > > > > > > > > > > > > > > > > > > > > > > > > > Den lördag 11 januari 2020 kl. 21:10:34 UTC+1 skrev Eram semper recta:
> > > > > > > > > > > > > > > > > > > > > > > > > > > Truly shocking that Messager admits he is wrong. See link below:
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > https://groups.google..com/d/msg/sci.math/WMyAFb-x-d4/8SIIukY5DwAJ
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > Study the article yourself to see exactly how significant is the geometric identity [f(x+h)-f(x)]/h = f'(x) + Q(x,h) that was dismissed out of hand by Messager and then confirmed to be TRUE:
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > You will see much knowledge you couldn't imagine even if you lived for thousands of years!
> > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > Please, your shite is nothing groundbreaking. It is rather trivial and most importantly, insufficient.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Yeah it's wrong. But, might as well confiscate whatever's right about it.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > "[f(x+h)-f(x)]/h = f'(x) + Q(x,h) "
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > The difference in x, over h, is f prime of x, and this "Q(x,h)".
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > The difference in x over h is f'(x) ?????
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > Um, no, it's not moron. [f(x+h)-f(x)]/h is the slope of the non-parallel secant line.
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > <PLONK>
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > The f' is the instantaneous rate of change, Q(x, h) is just a
> > > > > > > > > > > > > > > > > > > > > > > > > parameterized line, that also, is just a component of rise/run.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Taking the limit as h goes to zero is f', the derivative,
> > > > > > > > > > > > > > > > > > > > > > > > > for example according to standard calculus, this Q(x.h)
> > > > > > > > > > > > > > > > > > > > > > > > > is just "rise/run", the "over-taneous" component, it really
> > > > > > > > > > > > > > > > > > > > > > > > > seems just another take on a scribble of a notion of Newton,
> > > > > > > > > > > > > > > > > > > > > > > > > or maybe that's where there are ideas as least that somebody
> > > > > > > > > > > > > > > > > > > > > > > > > already had and here about in the 1700's with Isaac Newton
> > > > > > > > > > > > > > > > > > > > > > > > > about the summable areas being sawtooth jag instead of rectangles
> > > > > > > > > > > > > > > > > > > > > > > > > which these days is the usual.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Combined with some other howlers and let blind out to the
> > > > > > > > > > > > > > > > > > > > > > > > > Internet, the tortured howler fiend is quite assured that
> > > > > > > > > > > > > > > > > > > > > > > > > all its mathematics are that simple line turn.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > There are lots of ways to do calculus, it's any general
> > > > > > > > > > > > > > > > > > > > > > > > > application of exhaustion and for series, the real and
> > > > > > > > > > > > > > > > > > > > > > > > > here the standard real analysis with the differential
> > > > > > > > > > > > > > > > > > > > > > > > > caculus and integral calculus, for real numbers, is so
> > > > > > > > > > > > > > > > > > > > > > > > > widely used that they teach it in secondary school, and
> > > > > > > > > > > > > > > > > > > > > > > > > never get into Cesaro or the umbral calculus or the calculus
> > > > > > > > > > > > > > > > > > > > > > > > > of finite differences or any number of calculi like the
> > > > > > > > > > > > > > > > > > > > > > > > > yenri or a Newton's way or a Leibniz' way or Archimedes'
> > > > > > > > > > > > > > > > > > > > > > > > > or Aristotle's, there are all kinds of calculus, and
> > > > > > > > > > > > > > > > > > > > > > > > > really it's foundation is the exhaustion of 1 to 0 in measure.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > I.e., they already have measure, and use calculus for measure 1.0.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > The howler troll is just kind of straggled at a precipice
> > > > > > > > > > > > > > > > > > > > > > > > > of a few basic but irrelevant to each other notations of
> > > > > > > > > > > > > > > > > > > > > > > > > partial views of a bigger picture (here our "Poster Elephant").
> > > > > > > > > > > > > > > > > > > > > > > > > That it keeps trying to scratch others up there I'm not sure
> > > > > > > > > > > > > > > > > > > > > > > > > whether it believes or not.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > The integral calculus is a thing, it's used for the quadrature,
> > > > > > > > > > > > > > > > > > > > > > > > > and the differential calculus is used for gradient descent,
> > > > > > > > > > > > > > > > > > > > > > > > > there are lots of different "calculi" for those things, too.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > ("Calculi" is the plural of "calculus", there are "calculuses".)
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Besides, I discovered an axiomless geometry and clearly that's
> > > > > > > > > > > > > > > > > > > > > > > > > the fundamental measure 1..0 in my differential and integral
> > > > > > > > > > > > > > > > > > > > > > > > > calculus with the fundamental theorems of differential and
> > > > > > > > > > > > > > > > > > > > > > > > > integral calculus (including the standard one).
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Your ???? there is that "+Q(....)" there.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > So what? Q(x,h) is the difference in slopes of the non-parallel secant line slope and the tangent line slope. This is FACT from the geometry:
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > <drivel follows>
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Behold, Nimrod Gomer: great hunter chases his tail.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Not knowing what to read and besides not reading it there,
> > > > > > > > > > > > > > > > > > > > > > > it's a dummy of the crunch crunch crunch sort.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Besides, fundamental (diff. and int.) calculus arises from a
> > > > > > > > > > > > > > > > > > > > > > > spiral space-filling curve as a natural continuum.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > (There's also explanatory power and apologetics in
> > > > > > > > > > > > > > > > > > > > > > > foundations with set theory for this.)
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Can you show me how you find the derivative of for example f(x) = 2^x?
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > You can write 2^x as e^(x*ln2) and then it's pretty easy to do.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Don't be fooled by the idiot troll Christensen and his sidekicks Sergio and Burse.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > [f(x+h)-f(x)]/h = f'(x) + Q(x,h) is GEOMETRIC FACT. There is no debate over its truth.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > KON
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > That is a first step. Now, show me the rest!
> > > > > > > > > > > > > > > > > > > KON
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > What the hell, let's do it.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > f(x) = e^(x*ln2)
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > SLOPE FUNCTION is [f(x+h)-f(x)]/h:
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > [e^((x+h)ln2)-e^(xln2)]/h
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > = {1 + (x+h)ln2 + [(x+h)ln2]^2/2! + [(x+h)ln2]^3/3! + ....}/h
> > > > > > > > > > > > > > > > > > - {1 + xln2 + [xln2]^2/2! + [xln2]^3/3! + ...}/h
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > = {hxln2 + 2xh*ln2/2 + h^2(ln2)^2/2 + ... }/h
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > And what is this?
> > > > > > > > > > > > > > > > > Using infinite series?
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > I have only used series. There is no such thing as "infinite series". That is an illusion in your brain.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Is it allowed? In your mathematics.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Infinite series is not allowed in ANY mathematics and it's not a problem because it isn't used if it does not exist, yes?
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > KON
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > f'(x) = (2^x)ln2
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > And in your construction of the series, haven't you used what I asked you to show?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Listen idiot, you are annoying self all over again.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > You asked what is the way to find the derivative of f(x) = (2^x). I showed you moron!
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Then you carried on about infinite series which do not exist. When did I ever tell you that I reject series? NEVER. I reject the phrase "infinite series" because no series is "infinite". Nothing is "infinite". There is no such thing as "infinity". It's a bunch of crap. WHAT IS YOUR PROBLEM YOU FUCKING MORON????
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Learn to communicate properly. You whine and complain and then when I show you how it is done, you act like a fucking idiot that you are.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Now YOU know that [f(x+h)-f(x)]/h = f'(x) + Q(x,h) is true, but you are no different from the rest of the dishonest bastards on this newsgroup.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Unbelievable that you try to make up excuses in order to save your BOGUS calculus. Doesn't truth and logic mean anything to you any longer?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > > KON
> > > > > > > > > > > > >
> > > > > > > > > > > > > And I asked you if you use what (2^x)' is equal to in your evaluation of the series. If you do then it is a bit circular, don't you think?
> > > > > > > > > > > >
> > > > > > > > > > > > No. There is no circularity whatsoever. Series are valid mathematical objects. There are no infinite series, only series that converge.
> > > > > > > > > > > >
> > > > > > > > > > > > > KON
> > > > > > > > > > >
> > > > > > > > > > > If you deny it's circularity, then I will call it the never ending story :)
> > > > > > > > > > > I am now following Europen champ handball. Will come back to you.
> > > > > > > > > > > KON
> > > > > > > > > >
> > > > > > > > > > A follow up.
> > > > > > > > > > The question is find the derivative of the function f(x) = 2^x.
> > > > > > > > > > JG says [f(x+h) - f(x)]/h = f'(x) + Q(x,h).
> > > > > > > > > > He says it is simple because f(x) = e^(xln2). Which is fine.
> > > > > > > > > > Now he gives this:
> > > > > > > > > > [f(x+h) - f(x)]/h = [e^(x+h)ln2 - e^xln2)]/h, and give a series evaluation of this. There are some ellipsis missing, but what the heck.
> > > > > > > > > > I would do it like this (just to simplify) = e^xln2[e^hln2 - 1]/h.
> > > > > > > > > > Now he uses Maclaurin's evaluation of e^hlnx, and get the series.
> > > > > > > > >
> > > > > > > > > FALSE! The series e^x is obtained from a binomial and the function is given as:
> > > > > > > > >
> > > > > > > > > f(x,n) = (1+xn)^(1/n)
> > > > > > > > >
> > > > > > > > > e^x = f(x,0)
> > > > > > > > >
> > > > > > > > > The following article describes the complete derivation of e^x and there is ZERO calculus in it! I have shown you this before but you didn't pay any attention.
> > > > > > > > >
> > > > > > > > > https://drive.google.com/drive/folders/0B-mOEooW03iLUUlFR0ZwMjNNVjg
> > > > > > > > >
> > > > > > > > > > The problem is that this evaluation need to know in beforehand what (e^hln2)' is.
> > > > > > > > > > That is JG already knows what the derivative of 2^x is.
> > > > > > > > >
> > > > > > > > > Nonsense!
> > > > > > > > >
> > > > > > > > > > You have read what I gave you in another post?
> > > > > > > > >
> > > > > > > > > You write a lot of stuff - most of it wrong.
> > > > > > > > >
> > > > > > > > > > What I am saying to you is this:
> > > > > > > > > > You are using the derivative which is asked for to evaluate the derivative which is asked for.
> > > > > > > > >
> > > > > > > > > I do NOT use the derivative ANYWHERE in it. The series for e^x is derived WITHOUT any calculus as I explained earlier. It can be differentiated term by term.
> > > > > > > >
> > > > > > > > But this is not the series for e^x, but for e^(xln2), and they differ.
> > > > > > >
> > > > > > > Excuse me idiot? How do you think we find the series for e^(xln2) ? We find it after we have established differentiation which means you can use Taylor series which is FINITE, contrary to mainstream opinion.
> > > > > > >
> > > > > > > > I have copied this from earlier in this post written by you:
> > > > > > >
> > > > > > > "{1 + (x+h)ln2 + [(x+h)ln2]^2/2! + [(x+h)ln2]^3/3! + "
> > > > > > >
> > > > > > >
> > > > > > > > It has nothing to do with the binomial theorem. Taylor? Yes..
> > > > > > > > Someone mentioned BT and you get hooked!
> > > > > > >
> > > > > > > No moron. I was talking about 1/(x+h) which is (x+h)^(-1) and can be expanded using the binomial theorem.
> > > > > > >
> > > > > > > > KON
> > > > > > > >
> > > > > > > > >
> > > > > > > > > > Is that sound mathematics?
> > > > > > > > >
> > > > > > > > > What you do is not sound. What I do is very sound mathematics.
> > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > KON
> > > > > >
> > > > > > Yes, I am such an idiot :) Can you give me how you evaluate the series for 2^h?
> > > > > > Or should this continue forever?
> > > > >
> > > > > I have shown you, but you are a troll. I can use Taylor series once I have established the derivative using f'(x)+Q(x,h)=[f(x+h)-f(x)]/h and then find power series for 2^x. What's your problem????
> > > > >
> > > > > No idea what you are going on about. You need to learn to express yourself precisely.
> > > > >
> > > > > > KON
> > > >
> > > > Ok. I will explain.
> > > > I gave you f(x) = 2^x. And asked what is f'(x).
> > > > You give 2^x = e^xln2.
> > > > From this [2^(x+h) - 2^x]/h = [e^(x+h)ln2 - e^xln2]/h.
> > > > I think that here we agree.
> > > > Now e^xln2[e^hln2 - 1]/h = 2^x[e^hln2 - 1]/h.
> > > >
> > > > Isn't this just complicating things? You like it!
> > >
> > > No. There is a good reason I used the fact that 2^x = e^xln2 which requires ZERO calculus since e^x = f(x,0) where f(x,n)=(1+xn)^(1/n) and (1+xn)^(1/n) is expanded using the binomial theorem.
> > >
> > > You'd have a problem trying to divide by h taking the standard approach. Now we KNOW that f(x+h)-f(x) will have an h in EVERY term because this is proved here:
> > >
> > > https://drive.google.com/open?id=1X94DswLu89Ivtl415GvkQRBAonRei8Cj
> > >
> > > f(x+h)-f(x) = h * tan ( (pi/2) - arctan ( h/f(x+h) ) )
> > >
> > > Since h is a factor of every term on the RHS, it is also a factor of f(x+h)-f(x).
> > >
> > > We don't have to trip over our feet finding Q(x,h) for difficult cases because we know that we can simply SUBTRACT it from both sides of
> > > f'(x)+Q(x,h) = [f(x+h)-f(x)]/h.
> > >
> > > >
> > > > Why not [2^(x+h) - 2^x]/h = 2^x[2^h - 1]/h.
> > > > Now you only need to evaluate 2^h using whatever series you want. But be aware; to do it you need to know what the derivative of 2^h is (and '' ''' and so on).
> > > > I am asking; what use is it?
> > > > Because isn't the derivative of 2^h the same as finding the derivative of 2^x?
> > >
> > > You don't have to know the derivative of 2^h using the method I showed you.
> > >
> > > > KON
> >
> > Yeah so what, it is "the riddle of the contour integral",
> > then the terms in the squares, it is just establishing a "filling basis",
> > inventing that it's quadratic in terms, which he doesn't know. Or it.
> >
> > That's Newton Coates or Coates , Newton-Cotes, for me at least -
> > finding some basis and calling it ideal.
> >
> > I'd like to be him.
> >
> > 2^h and its derivative, with powers in sums,
> > is then for natural log is bigger than two instead of under two.
> >
> > (Natural logs in 2.)
> >
> >
> > Or, I can write logarithms in 0, 2, instead of zero, infinity.
> >
> > For which the natural logarithm is less than 3.
> >
> >
> > This though is filling the product space then for
> > example parametric equations of circles
> > as a scan over the sphere.
> >
> > I don't know what it rubbished itself
> > but there are all kinds of books full
> > of all kinds of mathematics to find out.
> >
> > Just to have some algebra cancellation
> > and build up the yenri,
> > besides building the corners into the sphere,
> > contour integrals are perfectly neat for that.
> >
> > 2^h is special because it's the logarithm,
> > but, it's the binary logarithm.
> >
> > e^h, natural exponent, which, e, is so valued,
> > if often for example usual 1 + 1/x, sum, that's
> > though that e is so valued.
> >
> > Compound interest adds up e, this example
> > in time and money helps makes sense the
> > "natural logarithm".
> >
> > Then with laws of arithmetic in logarithms,
> > logarithms for roots
> > have no shortages of books about them
> > and all what sort features of mathematics there are.
> >
> >
> > I'd be happy for it but of course
> > somebody already discovered all these things.
> > I am learning more about them now.
> >
> >
> >
> > Here this "put the integral in the binomial"
> > is besides just adding them together, in the model,
> > with the products of the polynomial, the coefficients,
> > that it's under that case only the "nil-square"
> > then for making those differential equations anyway.
> >
> > Or: "it's not the coefficients".
> >
> > The content is not so surprising,
> > just you find find lots more about it,
> > and these people never heard of JG, ever,
> > as if there isn't just another reason for
> > "G-d, an Internet troll finally read the Internet."
> >
> > The are connected howlers of totally ready mathematics,
> > here this dusty gem the bot rolled out.
> >
> > I.e., ready for somebody else.
> >
> >
> > I must imagine everybody knows the standard joke -
> >
> >
> > Guy's car tire flat on the road, pulls over to replace.
> >
> > Removes cap, lifts the car, wrenches off the nuts,
> > putting them in the cap, gets the tire on and
> > knocks the cap and is the nuts are lost. Can't
> > find the nut, can't wrench on the tire. Guy
> > shows up on the other side of a fence "hi I'm
> > a mental patient, if you lost the nuts from one wheel,
> > and can't find them, remove one of the nut from
> > each of the other wheels, and get it on.". And the
> > guy says , "if you're so smart, why are you in a mental
> > institution", and the guy says "I read how to do it on
> > the Internet".
> >
> > Here it's "why are you in a mental institution",
> > the guy says "I'm smart, not insane".
> >
> > I don't so much know, and,
> > I don't so much care, here what the JG bot has its toy.
> >
> > It's my toy, too.
> >
> > It was "why are you in a mental institution",
> > and "I'm insane, not stupid".
> >
> > That only works once - though.
> Seems it just figures if the slope is 1 then
> the secant at the tangent will only be a part
> of the circle under it.
>
> "Breaking the corners" then for numerical differences,
> just seems a neat usual integer basis, [0,2].
>
> Now the bot's never heard of "gradient descent".
>
> That's still "just" a line equation.
>
> Then, making those of integrals,
> is that it is just the cut, rest,
> cutting the right angles to 45's or the
> 60 in the middle.
>
> Counting arguments from models are
> usual piles of lines for example building
> piles of products.
>
> Dinner-conversation: infinity.
>
> Using the equivalency function to build the
> range [0,1] of the slope for Newton-style
> differencing (upward), it is not a tool so much
> just a feature, that it is the area component.
>
> Or, I'll get that out of it.
>
> Really it seems so usual that it's Newton-Fourier,
> I think it really helps to have an understanding of
> the history of development in mathematics, to be
> able to point to it and not have to care besides what
> other people make of it. Really I imagine there are
> very many examples of just developments of Newton
> or Euler then calling those for what they are, with
> their weaknesses why they are dusty today, just because
> it is another ancient proof of column circumference.
>
> Yeah, that's "calculus of finite differences" and "contour
> integral" here for some "slope integral", here "slop integral".
>
> The rise/run is just underdefined, it is often or usually though
> 1/0 or 0/1, just that it's 1/1 and so the area component is
> "defining" itself, _away_.
>
> I.e. really that's just like one of Newton's methods of integration,
> but there's a big difference between that and somebody else
> just demanding that it's its toy, that isn't the troll's, it's Newton's,
> and it's put aside because it's not generally applicable.
>
>
> Newton's troll.