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boolean functions return true or false or never halt: bool x() { return !x(); } and algorithms can't always decide which of the 3 it is: bool x() { return !returnsTrue("x()"); } Halting Problem |
propositions can be proven true or false or can't be proven: x := ¬x and math can't always prove which of the 3 it is: x := ¬provable("x") Gödel's Proof |
statements can be reasoned true or false or can't be reasoned: this statement is false and humans can't always reason which of the 3 it is: this statement is not true Strengthened Liar |