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Comment by pofilat | Hacker News Reader

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)

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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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