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bleistift2@sopuli.xyz ⁨1⁩ ⁨day⁩ ago

I find this axiomatization of the naturals quite neat:

  1. Zero is a natural number. 0∈ℕ
  2. For every natural number there exists a succeeding natural number. ∀_n_∈ℕ: s(n)∈ℕ (s denotes the successor function)

Now the neat part: If 0 is a constant, then s(0) is also a constant. So we can invent a name for that constant and call it “1.” Now s(s(0)) is a constant, too. Call it “2” and proceed to invent the natural numbers.

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