Complete Proofs
Well, I just stumbled upon this awesome site here.. They have proofs for essentially all of mathematics that go down to the axioms.http://us.metamath.org/mpegif/0.999....html
And hey, even a proof that 0.999... = 1. Fancy that. Ah well. Comment system should be up by Sunday morning (Pacific), and if it's not I'll eat...er, not eat my breakfast. (Hey, I can't commit myself too much on this can I?)
Posted on 2009-10-18 by Jach
Tags: math
Permalink: https://www.thejach.com/view/id/35
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Jach
October 18, 2009 06:54:43 AM
See? I got comments up. Timestamps ftw.
Jach
October 18, 2009 07:05:42 AM
Woops, timezone off. Ah well, should be fixed now.
Jach
October 18, 2009 07:06:26 AM
Or not. Eh, who cares. I set the timezone to US/Pacific, but it's saying it's 10am when in fact it's 7am.
Anonymous
October 18, 2009 07:13:59 AM
Hush. Non-JS people can enable it and conform or see the raw JSON.
Anonymous
February 04, 2013 07:48:50 AM
Note to self: the hyperreals won't save you. For one, any theorem on the reals applies to the hyperreals. Second, in order to create a construction in the hyperreals such that 0.999... is not 1, you have to throw out arithmetic, or reject the concept of decimal expansion resolving to anything. To see the first: let h be an infinitesimal such that 0.999... = 1 - h, implying 0.999... != 1 in this system. However, what is 1.999... = 1 + 0.999... ?=? 2 - h ?=? 2 - 2*h? As you can see, you can't do arithmetic this way, and indeed the equation is only properly resolved if h = 0.
