On 3/3/2014 12:13 AM, John Gabriel wrote: > On Monday, 3 March 2014 09:22:46 UTC+2, Roland Franzius wrote: >> Am 02.03.2014 20:46, schrieb email@example.com: > > <snip> > > Agree with previous comments. > >> For their proofs most of the corpus of formulas of elementary functions >> and higher transcendental functions need only one or two essential limit >> theorems about absolutely, equicontinuous convergence for derivatives. > > In fact, we don't need limits at all, as Newton showed. > > If f(x)=sin(x)/x, then f(0)=1. There are no limits here. The so-called "limit" is a fallacy, because f is exactly computable at x=0. >
Eh, that doesn't help you that in linearization as numerical method, just like Cotes', there is an error term (here as in examples where the error term vanishes).
No, these various methods, routines, or tricks a) don't contradict anything already in the calculus, b) use a subset of analysis and the calculus, also with that the results via Cotes are proved with standard real analysis, c) work on a subclass of continuous curves, and a quite general one, but not a general one, d) besides connecting to the line integral, as is built of the continuous function then to shade the space, which could have various functions in that, it is otherwise the bit disconnected from transformation of coordinates. Built as it is generously read to be, there are a variety of new sources of error terms and bias, in construction, then there are as from the usual orthonormal basis and the usual fundamental theorems of the integral calculus.
Besides, Gabriel's nettlesome or offensive enough, I don't see people in real life being such cretins without much expecting to eat their words or teeth. This, even along lines of simple truisms dashed with invective, it would be as easy to explain the fundamentals to another who would go about perhaps at least being conscientious in definition insofar as mathematical claim.
Or, "congratulations, that's 300 years old", and the reason it's not primary in mathematics is because it's not primary in mathematics.
That's firm and not unharsh, if you were arduous but instead forthright it would be easier to count you. Besides, if you expect it to develop greater connections to greater mathematics, as it has, unless you plan on setting up an answer shop for the perpetuity, it's forgotten.
Similarly I maintain that the sweep N <-> R[0,1] with f constant monotone, as is modeled by finite functions. There are undoubtedly others on that, for example any who ever saw [0,1] divided as points in order: the finite continuum.
So, while you claim priority on these, I am to the point where I point to Leibniz and say "this is what I say", Leibniz is among those who've defined this function, as for example Newton did with fluxions (not as nilpotent, but as not their own fluxions). Again in various regular definitions and modes of reason since antiquity, there is a working definition of this function since Man had infinite integers in one integer. Then, I have gone about establishing and exploring certain of its properties.
I find it ironic no-one else had. This based on imperfect information, I look forward to the day of finding great true extra-dogmatic features in mathematics, here as: they are. For, there are, and, in the foundations and in simplest developments and in first principle(s), there are: as primary.