Re:The Point of the Banach-Tarski Theorem
by camjw on Sunday January 22, 2023 @06:53PM
(#34483695)
It feels to me like you're redefining what a number is to be very different to what anyone with a maths background would say a number is. Essentially you're saying that neither e nor pi are numbers?
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Re:The Point of the Banach-Tarski Theorem
by moloch-hai on Sunday January 22, 2023 @07:29PM
(#34483947)
They are not numbers you have ever used in an actual calculation. You always approximate them anyplace they don't cancel out.
There is a countable subset of the reals called "computable numbers". We only ever use a subset of computable numbers in real calculations.
Re:The Point of the Banach-Tarski Theorem
by fellowmartian on Sunday January 22, 2023 @10:23PM
(#34485106)
in my view they never were "numbers" (as in constants), they are functions
Re:The Point of the Banach-Tarski Theorem
by andrewaylett on Monday January 23, 2023 @06:15AM
(#34487535)
The only numbers that may exist in nature are the non-negative rationals. Negative numbers are widely useful, but they don't exist in any meaningful way: they're an abstraction over reality. Irrational numbers definitely don't exist, and don't get me started on so-called "imaginary" numbers -- they're no less present in nature than the negative numbers are.
But the concepts are useful, and the symbols have meaning. The article mentions normal words having different meanings in mathematical language, and that impacts even every-day use of maths.