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But in an environment manipulating symbols where one of them 'x' has the property that multiplying by zero gives ten, I don't think the above sequence could hap
by grkvlt 12y ago
But in an environment manipulating symbols where one of them 'x' has the property that multiplying by zero gives ten, I don't think the above sequence could happen, or at least the symbolic evaluator would arrange things so that the first time it sees '0 * x' it replaces that with 10. So to evaluate the truth of the expression '(a+b) * x = 10' with 'a' and 'b' equal to zero, we just need to ensure the 'a+b' is evaluated to zero before the multiplication, using the axiom 'n+0=n' and we are back to '0 * x' on the LHS, which is ten.
I think it should be possible with appropriate precedence of the evaluation rules?
- Tloewald 12y agoRight, the same kind of arguments are the basis for calculus, and limit proofs work without being able to prove 1 = pi.
- klodolph 12y agoYou're turning something which is merely wrong into a total nightmare. Suddenly, 0+0 is not 0, because you have to wait to see if you multiply it by x first before you can evaluate 0+0! Now there are multiple distinct values for 0! Chaos and disharmony abound! In your system, 0+0=0+0, and 1+1=1+1. You can't simplify any of your equations! In your system, 1+1=2 is FALSE! No, seriously. Quit while you're ahead. Now that you know that dividing by zero and getting a result is not a logically consistent proposition, you can stop trying. That's the awesome thing about logic: once you PROVE something is impossible, you're done.