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Re: Halting Proof Fails
Kriminal, thank you, that makes for a much more engaging conversation... really does, seeing where you are coming from, helps build replies that cater to what it is that you seek.
The thing with math, as well as any science is the fact that the facts claimed are facts that are proven to any arbitrary case we can come up with at the current time. Not to be confused with theories, but you were not implying those anyways. These facts are to our understanding facts, axioms, something so fundemental to math that many later concepts are built on them. But like any science, and math is a science of numbers, in many things it is not certain, thus is prone to, and accepts change. Proofs are proofs, they prove the concept to some degree, some prove it to n'th degree, where for any value you can give it, the concept remains true, others are proven, sort of, beyond current reasonable doubt, though if your reasoning changes, the proof may fly out of the window. I think it takes an understanding of what science is to understand this difference between "facts" and "things we know"...
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