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Topic: § 454 Equality and the axioms of natural numbers
Replies: 30   Last Post: Mar 23, 2014 2:41 PM

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: � 454 Equality and the axioms of natural numbers
Posted: Mar 23, 2014 2:22 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <6e9a20e4-51cd-47f7-8588-6e07643b0df2@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Saturday, 22 March 2014 22:50:53 UTC+1, Virgil wrote:
> > In article <6d4210aa-0696-45da-b4ac-d80c55d6a4cb@googlegroups.com>,
>
> > Why should anyone else be required by WM to do what WM himself CANNOT
> > do, or at least never has done. namely successfully defend his own idiot
> > assertions.


> You are right that I never defended idiot assertions.

But you certainly have made enough of them.

> > The Peano postulates are accepted by the vast majority of mathematicians
> > in the world as being the skeleton of mathematical induction and that it
> > is by such an induction that the well-ordered set of natural numbers is
> > defined.

>
> That has been mentioned here frequently, but it is not an argument.


The fact that an idea is being widely accepted by mathematicians.
certainly argues that it is widely acceptable to mathematicians.

The fact that WM's idea are being widely rejected by mathematicians.
certainly argues thatthey are widely unacceptable to mathematicians.


> It is
> obvous to everybody whose brain has not been perverted or deleted completely
> that the Peano axioms do not define the natural numbers.


But they do define the essential properties of mathematical induction
without which properties the natural numbers would be much less useful.
>
> In principle it is without interest whether you understand that. But this
> discussion is a splendid demonstration of the fact that ridiculous but not so
> obviously foolish ideas like uncountable sets and undefinable numbers can
> exist in "modern mathematics".


Any sort of idea can and will exist in modern mathematics if enough
modern mathematicians are sufficiently interested in it, and both
uncountable sets and individually undefineable numbers are both such
ideas.
--




Date Subject Author
3/20/14
Read § 454 Equality and the axioms of natural numbers
heinrich.schliemann.ii@googlemail.com
3/20/14
Read Re: § 454 Equality and the axioms of natural numb
ers
JT
3/20/14
Read Re: § 454 Equality and the axioms of natural numb
ers
JT
3/20/14
Read Re: § 454 Equality and the axioms of natural numb
ers
JT
3/20/14
Read Re: § 454 Equality and the axioms of natural numbers
Dan Christensen
3/20/14
Read Re: § 454 Equality and the axio
ms of natural numbers
Robin Chapman
3/21/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/21/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/21/14
Read Re: § 454 Equality and the axioms of natural numbers
Ralf Bader
3/20/14
Read Re: § 454 Equality and the axioms of natural numbers
Dan Christensen
3/20/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/20/14
Read Re: § 454 Equality and the axioms of natural numbers
Dan Christensen
3/20/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/21/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/21/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/21/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/21/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/21/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/21/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/22/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/22/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/22/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/22/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/23/14
Read Re: ß 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/23/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/22/14
Read Re: § 454 Equality and the axioms of natural numb
ers
Dan Christensen
3/22/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/22/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/23/14
Read Re: § 454 Equality and the axioms of natural numb
ers
mueckenh@rz.fh-augsburg.de
3/23/14
Read Re: � 454 Equality and the axioms of natural numbers
Virgil
3/23/14
Read Re: § 454 Equality and the axioms of natural numb
ers
Brian Q. Hutchings

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