What does Banach-Tarki's paradox do to Euclid's system and proposition 7? — Gregory
The B-T paradox, as has been said several times in this forum, depends upon the Axiom of Choice. Not one of Euclid's. Sometimes the Axiom of Choice is involved in what are called "pathological" examples in mathematics. — jgill
The axiom of choice serves to make infinite sets behave as they should and is therefore the more natural choice than its negation — fishfry
Nice defense of the AOC ! [/url]
LOL. When I read that sentence in my mentions I thought I must have said something good about Alexandria Ocasio-Cortez in one of the political threads!
— jgill
Nice defense of the AOC ! [/url]
:cool: I think that those who spend time studying set theory and foundations have a much deeper appreciation for those subjects than do those of us who are briefly exposed to it and move on to different topics. It may have been a shift towards foundations the math department at the U of Chicago initiated back in the late 1950s that caused a rift with the physics department and resulted in physics students being required to take all their math courses in the school of physics. But I don't know how long that lasted; it may have been a temporary policy. — jgill
And without the AOC or something similar we wouldn't have non-measurable sets. :sad: — jgill
I think Banach-Tarski disproves common mathematics the way Godel set out to do (but failed). It breaks math — Gregory
What if they prove that you can take a greater object from a smaller? — Gregory
How is that much different than B\T? To me B\T says that is nothing discrete in geometry anymore — Gregory
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