Russell and Whitehead needed hundreds of pages to prove 1+1=2 — here's why
burny_tech · x · 2026-10-12
- In Principia Mathematica (1910), Whitehead and Russell spent hundreds of pages of logic before even stating 1+1=2, via proposition ∗54.43: with 1 defined as the class of all one-element classes and 2 as the class of all two-element classes, if α, β ∈ 1 then α ∩ β = ∅ ⟺ α ∪ β ∈ 2.
- Intuition: two different things make a couple; the same thing twice is still one (the accompanying diagram illustrates both cases with set pictures).
- Peano's axioms do it in one line: 1+1 = 1+S(0) = S(1+0) = S(1) = 2.
- Takeaway: the slow part wasn't the arithmetic — it was saying exactly what a number is.
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