On Sunday, 9 May 2021 at 12:13:52 UTC-4, timba...@gmail.com wrote:
> On Tuesday, May 4, 2021 at 11:45:59 AM UTC-4, Eram semper recta wrote:
> > On Tuesday, 4 May 2021 at 11:40:58 UTC-4, Eram semper recta wrote:
> > > On Tuesday, 4 May 2021 at 10:18:14 UTC-4, timba...@gmail.com wrote:
> > > > On Tuesday, May 4, 2021 at 7:48:19 AM UTC-4, Eram semper recta wrote:
> > > > > On Tuesday, 4 May 2021 at 07:22:44 UTC-4, timba...@gmail.com wrote:
> > > > > > On Tuesday, May 4, 2021 at 4:26:21 AM UTC-4, zelos...@gmail.com wrote:
> > > > > > > måndag 3 maj 2021 kl. 20:03:48 UTC+2 skrev Eram semper recta:
> > > > > > > > On Monday, 3 May 2021 at 01:17:14 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > fredag 30 april 2021 kl. 19:53:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > > On Friday, 30 April 2021 at 01:11:50 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > >Of course it is a *definition*. Cantor's entire diagonal gibberish argument requires that all numbers can be represented in a given radix system. In fact, the pitiful argument fails at the first step if this is not true
> > > > > > > > > > > The common one is notation dependent, the general one is however not.
> > > > > > > > > > In this case, notation is not even relevant.
> > > > > > > > > correct, notation is not relevant, it is only convenient.
> > > > > > > > Wrong. Notation is very relevant, only in this case it is not. Learn to read and pay attention to detail, you dimwit!
> > > > > > > Notation is not relevant, the object is. Notation is convinience for us humans to discuss said object.
> > > > > > Notation: forever irrelevant to Z means free pass for everyone to say anything anytime and its A-OK.
> > > > > > Z is always right, and I am always right, for our only difference is notation.
> > > > > > Make a note of it.
> > > > > > All that anyone ever wrote is notation, sir.
> > > > > > I think that what is important here is that we cover more ground, and as Z attempts to block such moves, then we are empowered to carry on our studies and frustrate him that much more...
> > > > > >
> > > > > > "As professor in the Polytechnic School in Zurich I found myself for the first time obliged to lecture upon the elements of the differential calculus and felt more keenly than ever before the lack of a really scientific foundation for arithmetic."
> > > > > > - https://archive.org/details/cu31924001586282/page/n13/mode/2up?ref=ol&view=theater
> > > > > About the only half-truth Dedekind wrote was this:
> > > > >
> > > > > ο άνθρωπος αριθμητήζει
> > > > >
> > > > > Lit: A human counts
> > > > >
> > > > > He failed to understand what it means. To make it a whole truth, one would write:
> > > > >
> > > > > Aριθμός είναι όνομα που δίνεται σε ένα μέτρο που περιγράφει ένα μέγεθος.
> > > > >
> > > > > Being the greatest mathematician alive today, I have revealed much more about the nature of the number concept and how my ancestors understood it, but were not quite able to express it as well as I:
> > > > >
> > > > > https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w
> > > > >
> > > > > Years from now, if the planet hasn't been blasted to smithereens, the above article will be worshipped as one of the most important ever written.
> > > > >
> > > > > And naturally, the most important book ever written:
> > > > >
> > > > > https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
> > > > "It is only through the purely logical process of building up the science of numbers and by thus acquiring the continuous number-domain that we are prepared accurately to investigate our notions of space and time by bringing them into relation with this number- domain created in our mind"
> > > > - https://archive.org/details/cu31924001586282/page/n43/mode/2up?ref=ol&view=theater
> > > >
> > > > Dedekind repeatedly references the human mind within his concerns around numbers. Of course this was at a time when any computing machinery was severely limited (in the late 1800s). Here though his sensibility to attempt to bring numbers in line with physics is a greatly underappreciated mode in this day when the divorce of these subjects so as to make room for more PhDs is several generations removed. Meanwhile electromagnetics was undergoing a flurry of activity right in this same generation.
> > > > Dedekind's sensibilities seem quite good from this translation. His concern over magnitude as a continuum concept and his focus to prove it is very fine. He seeks pure mathematics in perfect correspondence with Euclidean geometry. He does eventually go into operators as well, and his thinking is in line with the more modern abstract algebra whereby he does distinguish between the more pure sum and product versus their more problematic reversals.
> > > You're a bit of an idiot who sometimes is able to reach correct conclusions but you are infinitely stupid compared to me. I first read Dedekind's essay when I was between the ages of 11-14. I saw many issues with his approach but appreciated his honesty in stating that he didn't know. However, I soon lost respect for him as I continued to read. Much of D's drivel forms the basis of Cantor's set theory and also the theory of logic as understood by the incorrigibly ignorant mainstream mathematics academics.
> > >
> > > Let me start at the beginning with Dedekind's essay and give you a glimpse into the mind of how a genius thinks at the same time:
> > >
> > > "My attention was first directed toward the considerations which form the subject of this pamphlet in the autumn of 1858. As professor in the Polytechnic School in Zurich I found myself for the first time obliged to lecture upon the elements of the differential calculus and felt more keenly than ever before the lack of a really scientific foundation for arithmetic."
> > >
> > > Good on him that he realised his lack of understanding, but not so good that he was ignorant of the fact that a very sound foundation for arithmetic was already established in geometry. I know he later mentions "geometry" but he does so with a very superficial understanding of how arithmetic is directly derived from geometry. Of course, NO ONE after Euclid or before me even had a fucking clue about the meaning of ABSTRACT UNIT. Sure, they tossed it around almost as much as they do the word "intuition" whose meaning is a black hole in their minds. Get yourself a cup of coffee because you are not going to be able to understand my short response to you in only a few minutes. :)
> > >
> > > My ancestors realised that in geometry there is no actual <<unit>> other than a measuring tool. You see, Book 1 - 6 lays the foundations for Book 7 where the abstract unit (not in so many words because Euclid's definition of unit leaves much to be desired) was introduced. Book 5 in particular introduces arithmetic with <<magnitudes>>. In other words, you can perform any of the operations of arithmetic without even knowing what a <<number>> means. Allow me to illustrate this by means of some examples.
> > >
> > > ____ and ________ are distance magnitudes whose <<difference>> is the extension of the shorter line so that it matches the longer line.
> > >
> > > Their sum is the extension of the longer line by the length of the shorter line. So here you see two very simple examples of subtraction (the MOST primitive arithmetic operator) and addition that is possible because the shorter line is treated as a difference which must be applied to the extension of the longer line.
> > >
> > > So, even here we are already using requirements (NOT the bullshit you call axioms) to formulate the concepts of subtraction and addition.
> > > Notice there is no mention of <<number>>, only magnitudes - in this case <<distance>> magnitudes.
> > >
> > > Well, what about multiplication and division? It so happens that these operations are easily defined using angles in a circle that are subtended on the same arc. I have produced many videos on this topic so I won't waste time describing how it is possible in geometry to find an EXACT PRODUCT or QUOTIENT of ANY two MAGNITUDES in the universe. For the excessively ignorant math professors there is this video which explains:
> > >
> > > https://youtu.be/DG2pgnRFa8g
> > >
> > > In geometry the measure of the following two lines composed of equal lengths is DIFFERENT because in each case the equal part is used as the MEASURE or "unit". I leave a space between each equal part so that morons like you can understand:
> > >
> > > ____ ____ ____ ____ ____
> > >
> > > ________ ________ ________ ________ ________
> > >
> > > In geometry, we can do any of the operations of arithmetic on these lines without even an inkling of what the fuck is <<number>>.
> > >
> > > Now in algebra (as I was teaching Prof. Wolfgang Mueckenheim in recent weeks) we speak of a measure in terms of the ABSTRACT UNIT, that is, a unit whose SIZE or MAGNITUDE is irrelevant. We count each of the equal parts in each case to be the NUMBER 5.
> > >
> > > STOP! You need a few hours for this to sink into your ultra thick skulls. Once you are satisfied, then you can read on and learn more about how a genius thinks.
> > >
> > > "In discussing the notion of the approach of a variable magnitude to a fixed limiting value, and especially in proving the theorem that every magnitude which grows continually, but not beyond all limits, must certainly approach a limiting value, I had recourse to geometric evidences."
> > >
> > > Of course he would have to <<recourse>> to "geometric evidences" (moron Dedekind needed assurance from the true foundations) because ONLY geometry is the SOUND FOUNDATION of mathematics and in accordance with my 4 guidelines of well formedness:
> > >
> > > https://drive.google.com/file/d/0B-mOEooW03iLcy1FVGw4RHRibzg
> > >
> > > Naturally, the entire concept of limit in calculus (not really a part of calculus as much as it is a part of set theory) is utter rubbish, but as I have also written hundreds of articles on this topic, I refrain from writing more.
> > >
> > > "Even now such resort to geometric intuition in a first presentation of the differential calculus, I regard as exceedingly useful, from the didactic standpoint, and indeed indispensable, if one does not wish to lose too much time."
> > >
> > > Chuckle. Now D moves from "geometric evidences" to "geometric intuition" which of course is complete nonsense because there are no axioms in sound Greek geometry which is 100% the product of rational human thought:
> > >
> > > https://drive.google.com/file/d/0B-mOEooW03iLRjVxZERCa2R5Tlk
> > >
> > > "...but that this form of introduction into the differential calculus can make no claim to being scientific, no one will deny."
> > >
> > > Honesty from a mainstream academic is sooooooo refreshing. How sad that it is now extinct!!!! Quite clearly D realised that he didn't have a damn clue why calculus works and made no pretenses like modern academics do, in particular those who are most enlightened such as Prof. Wolfgang Mueckenheim and Prof. Norman Wildberger who are incorrectly compared to my great intelligence.
> > >
> > > "For myself this feeling of dissatisfaction was so overpowering that I made the fixed resolve to keep meditating on the question till I should find a purely arithmetic and perfectly rigorous foundation for the principles of infinitesimal analysis."
> > >
> > > Unfortunately Dedekind failed spectacularly as did anyone else in the history of humans who came before me. I was the first to produce a 100% rigorous formulation of calculus:
> > >
> > > https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
> > >
> > > The expressions "purely arithmetic", "perfectly rigorous" and "principles of infinitesimal analysis" are HUUUUGE (as scumbag Donald Trump would say) RED FLAGS.
> > >
> > > I am certain D intended the use of "purely arithmetic" in an effort to disassociate arithmetic from geometry. As I have explained, this cannot be done! Without the first 5 books of Euclid, you have NO arithmetic whatsoever. You don't even have a fucking idea what is a fraction or even a magnitude.
> > >
> > > The use of "perfectly rigorous" is a malpractice by thousands of academic morons since D's time. How can birdbrains even know what it means to be "rigorous" if they have no clue what it means for a concept to be well defined?!! LMAO.
> > >
> > > Finally, "principles of infinitesimal analysis" is a double faux pas since principles should never precede utter Newtonian delusions such as "infinitesimal analysis". This and much more bullshit is discussed and exposed in my free eBook for the incomprehensible and unbelievable rot that it is! So, you won't know until you study my free eBook.
> > >
> > >
> > > "The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explanation of this continuity is nowhere given; "
> > >
> > > Huge chuckles. Of course the most important theorem in calculus (mean value theorem) can be easily proved without knowing anything about "real numbers" which are a myth in every respect. Again, explained in my free eBook using the flawed tools of mainstream calculus and also the first rigorous formulation of calculus in human history - the NEW CALCULUS.
> > >
> > > "even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but, with more or less consciousness of the fact, they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never established in a purely arithmetic manner."
> > >
> > > Till this day the concept of continuity is circular and hence undefined in mainstream calculus. An unknown fact is that the methods of calculus DO NOT apply to any function that is not SMOOTH. From this we immediately understand that smoothness (includes continuity) is REQUIRED before one can even think about using calculus. In geometry, continuity is very well defined. See free eBook again.
> > >
> > > The idiot D again resorts to his favourite phrase "purely arithmetic".. Chuckle. My right eye hurts now so I have to stop.
> > >
> > > YOU ARE ALL FUCKING IDIOTS WHO HAVE NEVER UNDERSTOOD EVEN THE BASICS OF MATHEMATICS.
> > >
> > > Count yourself very fortunate that I bothered with this comment today!
> > What follows in Dedekind's laughable essay is his delusional belief that he succeeded to explain how he added "rigour" to his first found confusions to some insignificant nincompoop called Durege. So comical that it would be pathetic otherwise.
> >
> > What follows in the following chapters is too absurd and full of errors and contradictions that it would not be worth of my genius comment.
> >
> > Fuck yourselves! You ignorant, jealous, incompetent, stupid and arrogant nincompoops!