(September 25, 2009 at 3:04 pm)Tiberius Wrote: Well, 1 and 0.9r are different representations, but they have the same numerical value. Just as you can have a mathematical proof that 3/3 = 2/2, we have mathematical proofs that 1 = 0.9r.
Well that's what I mean, yeah. I just find it funny thinking of it as proof, because 2/2 is 3/3 by definition for example - so it seems more like explaining a tautology to me, that it actually being something to be proven. 2/2 is another way of representing the exact same number as 3/3, 1, or 0.9r, right?
Anyway, I understand. I understand that that's what mathematical proofs are, I just don't see them as stuff needed to be proven (at least not the examples above anyway), I see them more as tautologies needed to be explained to those who are ignorant of it.
@Retorth, I definitely like the continuity proof best, and I think all the other proofs become clear once you grasp that one. I love that.
EvF