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fiatjaf
on June 22, 2016
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Why isn’t the fundamental theorem of arithmetic ob...
Why is that chain of axiomatic proofs obvious? How is it obvious that one step follows the previous?
serge2k
on June 22, 2016
[–]
2 + 2 = S(S(0)) + S(1) = S(S(S(0)) + 1) = S(S(S(0)) + S(0)) - S(S(S(S(0 + 0)))) = S(S(S(S(0)))) = 4
Definiton of Successor (S) and addition. It's trivial.
fiatjaf
on June 22, 2016
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How is the definition of Successor so obvious, even if you explain it? How can I understand what it so obviously means?
serge2k
on June 22, 2016
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It's an axiom. We are talking specifically about 2+2=4 being trivial because it falls out of the axioms.
https://en.wikipedia.org/wiki/Peano_axioms
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