"The Lost Logic of Elementary Mathematics" Controversial Paper for Private Preview
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Thank you! Jonathan Crabtree
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Snippets from the 'Lost Logic of Elementary Mathematics...' follow:
If he were alive today, Euclid would be astounded. If Euclid could speak to us he would want everyone to know the above definition of multiplication is not his idea. Instead, it is the illogical invention of Henry Billingsley, a London haberdasher.
Astonishingly, Billingsley’s algorithmic definition of multiplication cited since 1570 is false, because it neither commutes nor computes.
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Co-Founder of Long-View Micro School; Co-Founder of The Number Lab
8 年Truth. And excellently conveyed.
Lead Analytics Engineer (Full Stack)
8 年Wow, no wonder education is crippled if this is what you people get excited about.
Grow Confident Construction Clients! #Predefine2020
8 年someone is lost, did the first para say who?when was it that we bumped into "streams of consciousness"? 1970's maybe? I think with this article i have just bumped into another. the stereograph - a wobble developed in my eye (as always with these) but i got there; saw the heading but after reading three pages i had lost track of what had been lost and i did not realise the euclid idea on page 4 was what could have been in opening paragraph. maybe my problem was that i got elementary maths in the fifties and Mira wasn't in any of my classes.
Founder and Head of Podometic Bharatiya Maths
8 年NOTE This follows on from a shorter article at https://bit.ly/NewMultiplicationViaEuclid and a YouTube video at https://www.youtube.com/watch?v=-NEYhIITHP4
Founder and Head of Podometic Bharatiya Maths
8 年Here's proof Math Dictionaries are wrong about multiplication. Quote: "...to multiply a by positive integral b is to add a to itself b times" https://www.collinsdictionary.com/dictionary/english/multiplication Via standard Grassman/Dedekind/Peano arithmetic... a x 1 = a b' = b + 1 ab' = a(b + 1) = ab + a (Note, this is the standard axiomatic definition of multiplication) Via me... ab + a = ab + a ab + a = a + ab ab = a + ab - a ab = a +a(b - 1) for all a and b ≥ 1 Therefore... ab = a added to itself b - 1 times (the French and American correction in the article.) NOT ab = a added to itself b times (Billingsley's bad 1570 idea, wrongly said to be Euclid's.) Note, in his Sur La Nature du Raisonnement Mathematique, [1] Henri Poincaré wrote: DéFINITION DE LA MULTIPLICATION Nous définirons la multiplication par les égalités a × 1 = a a × b = [a × (b – 1)] + a So ab = a added to itself b – 1 times. [1] Nature Du Raisonnement Mathématique Henri Poincaré, in Revue de Métaphysique et de Morale, T. 2, No. 4 (Juillet 1894), P. 377, Published by: Presses Universitaires de France https://www.jstor.org/stable/40891545