Re: Non-zero gaps between real numbers

On 03 Dec 2007 13:34:21 +0200, Phil Carmody wrote:
William Hughes <wpihughes@xxxxxxxxxxx> writes:
On Dec 2, 7:51 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:

Proove that the sum of measures of all real numbers in [0, 1] is equal
to 1.

The sum of all measures of all the real numbers in [0,1] is zero.

How are sums of uncountable numbers of things defined?

By considering the net of finite sums, ordered by inclusion. An
uncountable sum may exist only if all but countably many terms are zero.


--
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case heard May 17
U.S. Court of Appeals, Third Circuit
<http://www.abu-jamal-news.com/>
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