It seems odd to me to say that 0.999... = 1 is a "definition". I would certainly consider it a theorem. It can be proven in any axiomatization of the real numbers. The 19th century yielded the first clear constructions of the reals. People were summing infinite series well before Cantor. On Thu, Nov 15, 2012 at 1:54 AM, Dan Asimov <dasimov@earthlink.net> wrote:
I think Cauchy laid to rest any questions about the concept of time being an aspect of the concept of convergence.
--Dan
On 2012-11-14, at 9:51 PM, Gary Antonick wrote:
unless I'm missing something, there would still be the following problems: Zeno's arrow will never actually hit the tree (eg 1/2 + 1/4 + 1/8 will never quite get to 1) a polygon with more and more sides will not quite ever become a circle 9/10 + 9/100 + 9/1000 etc will not quite ever equal 1
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