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From the title and the original question in the article I expected something like a proof in a system of formal arithmetic, maybe a discussion of the Peano axio
by infinity 15y ago
From the title and the original question in the article I expected something like a proof in a system of formal arithmetic, maybe a discussion of the Peano axioms or a discussion of different possible representations of the natural numbers using sets (like von Neumann ordinal numbers) and the really interesting question if numbers are sets.
http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms
- dkarl 15y agoA short answer that sidesteps the question of what numbers "are" is that if two is 1+1 and four is 1+1+1+1 then it follows from the associativity of addition: 2 + 2 = (1 + 1) + (1 + 1) = ((1 + 1) + 1) + 1 = 4
- egiva 15y agoWell, the post wasn't very well written probably, but you can argue that they are talking about two concepts: Axioms and Notation. If you used base 2, or base 3 (or base -2, -3) math, then that particular notation would work out differently than, say, base 8 math, etc. For Axioms, here you go: http://en.wikipedia.org/wiki/Axiom http://en.wikipedia.org/wiki/Axiom