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Mathematics
General Math
Let's remove one axiom from Euclidean geometry
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[QUOTE="jedishrfu, post: 5887757, member: 376845"] The way you'd have to approach this is how specific theorems of Euclidean Geometry are affected when you remove a postulate. [URL]http://mathworld.wolfram.com/EuclidsPostulates.html[/URL] As am example, there was a time when people tried to remove the parallel postulate and prove it from the other four but they all failed. Later it was determined that new geometries resulted from a relaxation of the parallel postulate. [URL]https://en.wikipedia.org/wiki/Parallel_postulate[/URL] Off hand, I can't see the affects that removing the circle or allowing for multiple circles would have on the geometry. Perhaps looking at ordered geometry or absolute geometry will give you some insight: [URL]https://en.wikipedia.org/wiki/Ordered_geometry[/URL] [URL]https://en.wikipedia.org/wiki/Absolute_geometry[/URL] [/QUOTE]
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Mathematics
General Math
Let's remove one axiom from Euclidean geometry
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