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Comment by jkabrg | Hacker News Reader

I'll add that the significance of the formula is it's similar to

  a*b + a*c = a*(b + c)

which you ought to remember from school as "factoring/factorization". Except in this case, " * " is replaced with "V", and "+" is replaced with "->". In mathematics, you call that a "distributive law". Some more examples are

  a^c * b^c = (a*b)^c
  p/\q V p/\r = p/\(q V r)
  (pVq) /\ (pVr) = pV(q /\ r)

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While you're absolutely right that this is a kind of distributivity, conventionally + is related to "or", * to "and", and ^ to "implies". So the theorem as given would be rendered as something more like "(p + r)^(p + q) implies (p + r^q)".

That's interesting.... + and * theorems correspond between logic and arithmetic, but taking ^ as implication generates theorems that are true in logic but not in arithmetic.

(The truth table of implication is clearly different from binary exxponentiation)

Is it? I checked before commenting (because I also wanted to make sure the arithmetic analogy actually held):

    irb(main):001:0> 0**0
    => 1
    irb(main):002:0> 0**1
    => 0
    irb(main):003:0> 1**0
    => 1
    irb(main):004:0> 1**1
    => 1

Notice that `p -> q` becomes `q^p`, i.e. the operands swap position.

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