```Date: Mar 15, 2013 12:13 PM
Author: William Hughes
Subject: Re: Matheology § 224

On Mar 14, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:<snip>>... consider the list of finite initial segments of natural numbers>> 1> 1, 2> 1, 2, 3> ...>> According to set theory it contains all aleph_0 natural numbers in its> lines. But is does not contain a line containing all natural numbers.> Therefore it must be claimed that more than one line is required to> contain all natural numbers. This means at least two line are> necessary. There are no special lines necessary, but there must be at> least two. In this case, however, we can prove, by the construction of> the list, that every union of a pair of lines is contained in one of> the lines. This contradicts the assertion that all natural numbers> exist and are in lines of the list.Nope.Nope, two lines are necessary but not sufficient.Two lines can never do a better job than 1.Any finite number of lines is necessary but not sufficient.Any finite number of lines can never do a better job than 1.An infinite number of lines is necessary and sufficientAn infinite number of lines can do a better job than 1[In potential infinity things goAny number of findable lines is not sufficientAn unfindable line is necessary and sufficientAn unfindable line can do a better job thanany number of findable lines.]
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