Re: .99999... still=/= 1

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 12/08/04 

Date: Thu, 09 Dec 2004 00:06:51 +0100

panoptes@iquest.net (Daniel W. Johnson) writes:

> Richard Tobin <richard@cogsci.ed.ac.uk> wrote:
>
>> In article <1102464291.888947.41540@f14g2000cwb.googlegroups.com>,
>> John Schoenfeld <j.schoenfeld@programmer.net> wrote:
>>
>> >a(b+c) = ab + ac {Distributive}
>> >a(b+c+d) = a(b+(c+d)) {Associative}
>> >It follows that a(b_1+ ... + b_n) = a b_1 + a (b_2 + ... + b_n).
>>
>> Very good. Now prove the limit case.
>>
>> -- Richard
>
> Tell us which definition of limit you prefer, and we'll prove that
> a (lim_{n -> oo} k_n) = lim_{n -> oo} (a k_n)

*Given* that the limit on the left hand side exists.

No one doubts the truth of this theorem. The doubt is whether the
theorem is obvious from the distributive law alone, with no extra
argument needed. 

-- 
Jesse F. Hughes
"That's what's brutal about mathematics!  When you're wrong, you can
have spent years, and lots of effort, and come out at the end with
nothing." -- James S. Harris on the path of self-discovery (?)

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