There’s more to mathematics than rigour and proofs (2007)

Re:There’s more to mathematics than rigour and proofs (2007) by l33t2328 on Wednesday April 20, 2022 @08:41AM (#31095997)

I mean that for any epsilon > 0, you can have a set of intervals of the form (a_i, b_i) where every rational number is in some interval and the sum over all i of b_i - a_i < epsilon.

That is, you can cover the rationals with intervals of arbitrarily small total length.

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Re:There’s more to mathematics than rigour and proofs (2007) by auggierose on Thursday April 21, 2022 @09:04AM (#31108827)

I see. But is that not just a simple conclusion of the fact that the rationals are countable, and that there exists a converging series of positive numbers?

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Re:There’s more to mathematics than rigour and proofs (2007) by l33t2328 on Friday April 22, 2022 @12:19PM (#31123639)

Right but explaining why the reals are different is the tricky part

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