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Topic: Can L(<) be the language of the naturals?
Replies: 35   Last Post: Sep 10, 2013 2:12 AM

 Messages: [ Previous | Next ]
 albrecht Posts: 1,136 Registered: 12/13/04
Re: Can L(<) be the language of the naturals?
Posted: Sep 6, 2013 2:17 AM

On Monday, September 2, 2013 8:19:41 AM UTC+2, Albrecht wrote:
> Am Montag, 2. September 2013 05:11:09 UTC+2 schrieb Virgil:
>

> > In article <l0023u\$jol\$1@news.albasani.net>,
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> > Peter Percival <peterxpercival@hotmail.com> wrote:
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> > > Virgil wrote:
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> > > > In article <kvvu1c\$b1j\$2@news.albasani.net>,
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> > > > Peter Percival <peterxpercival@hotmail.com> wrote:
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> > > >
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> > > >> David Hartley wrote:
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> > > >>> In message <52236CD3.1030800@osu.edu>, Jim Burns <burns.87@osu.edu> writes
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> > > >>>> If I say that I have a set with a semi-infinite,
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> > > >>>> discrete, linear order, (N, <), is that enough to
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> > > >>>> define the naturals?
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> > > >>>
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> > > >>> I'm afraid not. Thee are many other orderings satisfying your axioms.
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> > > >>> E.g. N + Z - i.e. a copy of N followed by a copy of Z.
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> > > >>
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> > > >> Also, there is no recursive set of first order axioms that will capture
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> > > >> just the natural numbers.
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> > > >
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> > > > What's wrong with the von Neumann model?
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> > >
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> > > What I meant was, there is no first order theory T such that all models
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> > > of T are isomorphic to the (von Neumann, if you wish) natural numbers.
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> > > The upward Löwenheim-Skolem theorem tells us so.
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> > > If you want categoricity, you will need a second (at least) order theory.
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> > AS far as I can see, {} and x -> x\/{x} captures JUST the natural
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> > numbers and nothing else, and any other basis captures more.
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> >
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> > --
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> Your so called "natural numbers" are not the natural numbers of 99% of men. Why calling it "natural numbers" in spite of that fact?
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> The natural numbers of normal people starts with an object or entity or sign and increases in succesive adding further objects or entities or signs step by step.
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> E.g.:
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> I
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> II
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> III
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> IIII
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> IIIII
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> IIIIII
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> ...

Nobody answers the question why mathematicians call their Dr. Frankenstein creature |N natural numbers?

The natural numbers are exact that numbers which are written with a first object which depicts the first number which consists of one object, with a second object which depicts the second number which consists of two objects, with a third object which depicts the third number which consists of three objects, and so on.

This concept is ingenious and perfect. There is no better concept. This are the real and only natural numbers.

Anybody who calls something else "natural numbers" is a spoiler or a dummbatz.

Date Subject Author
9/1/13 Jim Burns
9/1/13 Jim Burns
9/1/13 David Hartley
9/1/13 Peter Percival
9/1/13 Virgil
9/1/13 Peter Percival
9/1/13 Virgil
9/2/13 albrecht
9/6/13 albrecht
9/6/13 Robin Chapman
9/6/13 Tucsondrew@me.com
9/6/13 LudovicoVan
9/6/13 Tucsondrew@me.com
9/7/13 albrecht
9/6/13 Michael F. Stemper
9/7/13 albrecht
9/6/13 FredJeffries@gmail.com
9/7/13 albrecht
9/7/13 FredJeffries@gmail.com
9/8/13 albrecht
9/6/13 Robin Chapman
9/6/13 Brian Q. Hutchings
9/7/13 albrecht
9/6/13 LudovicoVan
9/7/13 albrecht
9/7/13 LudovicoVan
9/8/13 albrecht
9/8/13 LudovicoVan
9/8/13 albrecht
9/9/13 LudovicoVan
9/10/13 albrecht
9/1/13 Jim Burns
9/2/13 Shmuel (Seymour J.) Metz
9/2/13 Shmuel (Seymour J.) Metz
9/2/13 Shmuel (Seymour J.) Metz
9/2/13 Peter Percival