Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
mueckenh@rz.fh-augsburg.de

Posts: 15,330
Registered: 1/29/05
Re: § 454 Equality and the axioms of natural numb
ers

Posted: Mar 22, 2014 5:20 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Saturday, 22 March 2014 19:57:44 UTC+1, Dan Christensen wrote:
> On Friday, March 21, 2014 2:41:17 AM UTC-4, muec...@rz.fh-augsburg.de wrote:
>

> > On Thursday, 20 March 2014 22:35:55 UTC+1, Dan Christensen wrote:
>
> >
>
> >
>
> >
>
> > > The real numbers can also be constructed from Peano's axioms.

>
> > That was not the question.
>
>

> > > It should be
> > > possible to prove than no irrational number is equal to a natural number.

>
>

> > That was not the question.
>
> You wanted to know if it was possible to prove, starting from Peano's axioms, that pi (or any other irrational number?) is not equal to a natural number.


No, here you can read the original question:
>
> > The question was: If the five truncated Peano axioms, not more and not less, define the natural numbers, as you said, what part of the axioms excluded that pi is a natural number?
>

> You are grasping at straws, WM. Again, the Peano axioms are just the 5 essential properties of the natural numbers from which it seems all others can be derived.

Of course everything can be derived by adding suitable definitions (like "0 = 1" or like "the difference between two successors is always the same and is called a unit"). But you said that your five truncated axioms, ***not more and not less***, are sufficient to define the natural numbers. Now defend that assertion or drop it.

Regards, WM


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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.