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Re: Halting Proof Fails
I can certainly provide an example.
Euclid's Parallel postulate states, well rather Playfair's rendition of that postulate states that at most one line can be drawn through any point not on a given line parallel to the given line in a plane. It is and remains an axiom, however the further mathematicians looked at space, and the fact that it is not always, or nearly ever is it flat, that concept had to be changed later, when looking at non-flat spaces, and planes that bend and curve, the geometry that made many current physics theories possible that axiom had to be changed to accommodate a new way at looking at things, where the Euclidean postulate still holds true for it's range, a postulate stating that more than one line that can be extended through any given point parallel to another line of which that point is not part, is one of the fundamental postulates in non-euclidean geometry (i.e. elliptic curve and hyperbolic geometries).
This is an example of how something once thought to be true, while still being true, had to be changed to suit a different theory of looking at things.
By the way, both postulates hold true, it just depends on which perspective you look from...
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