```Date: Nov 22, 2012 3:54 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!

On 22 Nov., 20:22, William Hughes <wpihug...@gmail.com> wrote:> Note that I was able to handle your> "simple" case using induction.>> I consider the following case easy.> If you disagree maybe you can say> why?>> Consider the sequence of real numbers>> 1.0> 10.0> 100.0> ...>> The limit is oo (unbounded)>> According to set theory, the number of 1's in the limit> is 0.  (The limit of the set of positions at which we> have a 1 is the empty set).Why should the 1 disappear completely? But let's assume it.According to analysis the number of 1's in the limit is 1 and thenumber of zeros left to the point is infinite. Proof by failure: Tryto establish in analysis the limit oo without 1 by the sequence000000...>> Your contention:  This is a contradiction.  You cannot get oo>                   with only 0'sMy contention is same as before: Obviously set theory cannot reproducethe results of analysis.>> My contention:   The two limits are different and there is>                  no contradiction.You try to justify one error by another one. Set theory cannotreproduce mathematics. That fact is not mended by constructing anotherfailure. But you see it better here> > 01.> > 0.1> > 010.1> > 01.01> > 0101.01> > 010.101> > 01010.101> > 0101.0101> > ...where set theory yields no digit and analysis yields inifinitely manydigits left to the point.Taking the result of set theory seriously, we get a limit less than 1.And in your example we can get rid of a 1 and have a limit oo withonly zeros. Do you think to defend set theory by that arguing? Shouldreally somebody take it seriously? And apply it anywhere? I don'tbelieve so.Regards, WM
```