Re:There’s more to mathematics than rigour and proofs (2007)
by Koshkin on Tuesday April 19, 2022 @08:41PM
(#31091365)
Well, to understand an explanation one must already know something, otherwise first you have to explain those other things, e.g. the simple fact that unlike the reals the set of rational numbers is countable…
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Re:There’s more to mathematics than rigour and proofs (2007)
by l33t2328 on Tuesday April 19, 2022 @09:07PM
(#31091540)
Cardinality hasn’t much to do with it since there are uncountable sets which you may cover like that.
Re:There’s more to mathematics than rigour and proofs (2007)
by Koshkin on Wednesday April 20, 2022 @07:35AM
(#31095387)
Sure, but for countable subsets (such as the rationals) it is easy to show.
Re:There’s more to mathematics than rigour and proofs (2007)
by l33t2328 on Wednesday April 20, 2022 @11:23AM
(#31098256)
Sure. Explaining what’s different about the reals is the hard part
Re:There’s more to mathematics than rigour and proofs (2007)
by Koshkin on Wednesday April 20, 2022 @06:36PM
(#31103971)
How so? Even a real interval of a finite length cannot be covered by any set of intervals of a smaller total length. (Unless the person you are trying to explain this to starts raising questions about the meaning of 'interval' or 'length', in which case the meaning of the original question becomes just as uncertain in the first place.)
Re:There’s more to mathematics than rigour and proofs (2007)
by l33t2328 on Thursday April 21, 2022 @11:00AM
(#31110316)
> Even a real interval of a finite length cannot be covered by any set of intervals of a smaller total length.
You’ve only restated the problem without saying _why_ covering the reals is different.