limits are icky, what is the patrician method to derive calculus?
https://en.wikipedia.org/wiki/Discrete_calculusthis is the true calculus that's used, and has been used for hundreds of years before autistic antisocial mathematicians invented the epsilon-delta formalism that plagues modern mathematics.>be mathematicians>invent (discrete) calculus>voila this shit is AWESOME>be schizo mathematician>say it's all useless>invent limits>invent (infinitesimal) calculus>formalize it to hell>look, so elegant!>all internally consistent proofs!!>be applied mathematician/physicist/engineer>huh, how the fuck do i program this bullshit? it's useless!>lemme just discretize these equations >mfw calculus was more useful before infinitesimal schizphrenia>mfw calculus is more useful in an applied sense with discretization >mfw i have no face
>>17012983just expand f(x+h) and grab what you want
>>17012983just because you don't know analysis doesn't mean it's concepts are icky
>>17012987there is no way I'm summing billions of discrete boxes>>17012983it's not that bad. If you want some ugly horse shitting smoke, look up Lebesque integrals.
>>17012983https://www.marxists.org/archive/marx/works/1881/mathematical-manuscripts/index.html
>>17012987
>>17012983infinitesimals or hyperreal numbers
>>17012987You’re half right.They should teach the discrete calculus before introducing infinite continuous limit expressions, not the other way round.
>>17012983non-standard analysis
>>17012983>limits are icky, what is the patrician method to derive calculus?The following is an excerpt from Peter J. Olver's alternative calculus lecture notes (https://www-users.cse.umn.edu/~olver/ln_/cc.pdf):>"I started thinking about the topological definition of continuity, [12]. In brief, a function is said to be continuous if and only if the inverse image of any open set is open. This sounds very simple — and certainly simpler than the limit-based definition used in calculus. And I started wondering why not try to develop basic calculus using this as the starting point, and, possibly, eliminating all references to limits, epsilons, and deltas while still retaining rigor. And, after some thought, I realized it could be done. Continuity is basic, and limits, including limits of sequences, and derivatives follow from it in a reasonably straightforward manner, while bypassing epsilons and deltas entirely! You will see the results of this line of reasoning below.>Not only can the development be made completely rigorous, I believe it is more elementary and eminently more understandable by the beginning mathematics student, who will be better able to appreciate the rigor behind the calculational tools. Moreover, this approach introduces them to the basics of point set topology at an early stage in their mathematical career, rather than having to start from scratch in a later course in the subject or in preparation to study real analysis".I sure hope the "new calculus" of the distant future, "Neo-Stewart", will be something along this lines, maybe together with some non-standard analysis (lie R. F. Hoskins https://archive.org/details/standardnonstand0000hosk). You could also try "naive infinitesimal calculus", like https://intellectualmathematics.com/calculus/
>>17012987non-standard analysis is perfectly legible. quit being a bitch.
>>17013332What if I don't believe in ultrafiters?
>>17013727Maybe you can believe in topos theory and intuitionistic logichttps://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis
>>17013332>infinitesimals or hyperreal numbersthose just use the standard definition of real numbers but unnecessarily layered into themselves over and over again like a retarded croissant.>>17013445>non-standard analysissee above>>17013634>non-standard analysissee above>>17013679>non-standard analysissee above
>>17012983Miles Mathis has a novel approach and also a criticism of the usual derivation. He also uses delta symbols to represent difference. It's a very clean notation.http://milesmathis.com/are.html
>>17012987You got the mathfags squealing with this lmao
>>17013763that's a known crank
>>17013847here's an updoot for ye!
>>17014229Why don't you read what he has to say and decide for yourself, rather than appealing to some unknown authority like a stupid little bitch.
>>17014264I did read it. How do you think I determined he was a crank? If you assume I based it off the opinions of others, you're projecting =]
>>17014265You literally said "a known crank". You didn't give any reason for why you think he's a crank.
it's autonomously closed algebroids with derivations
>>17014270>thinkCute language. I don't "think" he's a crank. I know he's a crank. So do many others.
>>17014350>I know he's a crank.How?>So do many others.Who?
>>17014359I'm going to be honest with you, man. The two answers are both trivial.>How?If you don't know, then you don't belong on this board. No amount of explanations on my end will help you understand. In other words, this is about as retarded as claiming the Earth is flat. I cannot convince you with physics, because you're too much of an overconfident, uneducated dipshit. >Who?Literally anyone with a baseline education in mathematics. That is to say, anyone who has completed a bachelor's in mathematics or higher.
>>17014365>this is about as retarded as claiming the Earth is flatWhat specifically about his argument is as retarded as claiming the Earth is flat?
>>17014367LMAO! That is not even close to what I was arguing. I was arguing that YOU are as delusional as a flat Earther. I can now conclude that you're as intelligent as one, too.
>>17014378You write like an LLM instructed to be as obnoxious as possible.
>>17012987Insanely based post
>>17012987FPBP>be me doing my degree in whatever>take course on scientific computing>things are only useful on discrete form>everything else is gay and jewish
>>17012983What was this shizo's name who in the 19th Century calculated the Orbit of Neptun before the planet was even observed through a telescope, whithout even an abacus. Anyway, I have started applying this method and so far I have become as capable as calculating the square root of any given number in my head.
