```Date: Feb 20, 2013 11:29 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 20 Feb., 13:31, William Hughes <wpihug...@gmail.com> wrote:> On Feb 20, 12:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > On 20 Feb., 11:30, William Hughes <wpihug...@gmail.com> wrote:> <snip>> > > A  statement you can make is that there> > > is no line of the list with the property> > > that it is coFIS to d.> > > (you do not need every line or every FIS to "actually> > > exist" to make this statement)>> > You need all FISs of d to make this statement.>> No, for each line of L you only need some> of the FISs.  For every line you need every> not all.Then you have a statement for finitely many lines and none forinfinitely many lines.>> <snip>>> > > Let z be a potentially infinite sequence such that> > > for some natural number m, the mth FIS of> > > z contains a zero.>> > > Are z and x coFIS?>> > No.>> Is the following statement true>> For every natural number n we have>>     the (n+1)st FIS of the nth line>     of L contains a 0.Of course. Similarly we have "for every natural number there areinfinitely many FIS of infinitely many lines that do not contain a 0".Again: Do not confuse every and all.After "all natural numbers" no natural number is following.After every natural number, there are infinitely many natural numbersfollowing.Regards, WM
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