```Date: Mar 25, 2013 12:57 PM
Author: fom
Subject: Re: Matheology § 224

On 3/25/2013 6:26 AM, WM wrote:> On 24 Mrz., 22:35, Virgil <vir...@ligriv.com> wrote:>>>>> The theorem does not cover what will transpire when two or more lines,>> along with all their predecessors, are removed.>> There is no reason to remove more than one line with all its> predecessors, because it can be proved that all lines are predecessors> of a line, since there is no line without follower.>>Once again, you have *proven* nothing.>> So it is of some interest to note that for any set of lines having a>> maximal line in it,>> Does induction not hold for the infinite set of naturals?> Or is there a maximal element in that set?> Or what else can be argued?http://en.wikipedia.org/wiki/SophismYou should try stating some precise mathematicalcontent.  Your readers are entitled to statementsthat can be judged in relation to existingmathematics.This game of introducing irrelevant questions impedesthem from doing so.>>>>> It is easy to see we know what>>>> will happen if we remove a natural>>>> number of finite lines.>>>>>> However, we do not know what will happen>>>> if we remove an infinite number of>>>> finite lines.>>>>> That's why we use induction.>>>> Except that no inductive argument will go from removing a finite set of>> lines to removing an infinite set of lines,>> Induction holds for the infinite set of naturals and for the infinite> set of lines. Otherwise it would be superfluous.Your use of induction *is* superfluous.One can follow the definitions of classical mathematics.One can follow the definitions of constructive mathematics.You do neither.Nor will you delineate your own definitions in spite ofbeing asked repeatedly.
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