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this post was submitted on 01 Oct 2025
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What's missing here os the definition that we're working in base 10. While it won't be a proof, Fibbonaci has his nice little Liber Abbaci where he explains arabic numerals. A system of axioms for base 10, a definition of addition and your succession function would suffice. Probably what the originals were going for, but I can't imagine how that would take 86 pages. Reading it's been on my todo list, but I doubt I'll manage 86 pages of modern math designed to be harder to read than egyptian hieroglyphs.
That ‘86 pages’ factoid is misleading. They weren’t trying to prove that 1+1=2. They were trying to build a foundation for mathematics, and at some point along the way that prove fell out of the equations.
Yeah, I assumed. No way 86 pages are needed for a proof of '1+1=2'.
That being said, it'd be nice for there to actually be a "proof" of 1+1=2, made as concise and simple as possible, while retaining all the precision required of such proof, including a complete set of axioms.
This, obviously isn't is, nor does it try to. It's not the "1+1=2" book, ot's the theoretical fpindations of matheđatics book. Nothing wrong with that.