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They most certainly are real proofs. However, they are a different _kind_ of proof if you mistakenly believe that only algebra can yield proofs. Provided you ha
by TheRealPomax 9y ago
They most certainly are real proofs. However, they are a different _kind_ of proof if you mistakenly believe that only algebra can yield proofs. Provided you have the algebraic rules for the type of geometry you are working with, any geometric proof can be expressed as algebraic proof and vice versa, but the trick is to appreciate that depending on what needs to be proven, one can represent in a single step what the other takes many tedious pages of step upon step upon step. And that goes both ways of course.
- adamnemecek 9y agoOfc, geometrical proofs are technically algebraic proofs (due to Homotopy type theory) but that's neither here nor there.
- TheRealPomax 9y agoYou don't get the luxury of hand waiving: the two are equivalent, and thus any rigorous proof in one has an equivalent proof in the other. In acknowledging this, you accepted your original claim was false. So what you really meant here was: "Ofc, geometrical proofs are technically algebraic proofs (due to Homotopy type theory). I must have had a brain fart when I implied that one could be more, or less real than the other. That made no sense."