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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 ]
 LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: Can L(<) be the language of the naturals?
Posted: Sep 6, 2013 3:35 PM

"Albrecht" <albstorz@gmx.de> wrote in message

> 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.
>
> E.g.:
>
> I
> II
> III
> IIII
> IIIII
> IIIIII
> ...

What is wrong with this?

|0| = |{}| = 0
|1| = |{0}| = 1
|2| = |{0, 1}| = 2
|3| = |{0, 1, 2}| = 3
...
|n| = |{i < n}| = n
...
|w| = |{i < w}| = w (i.e. aleph_0)

An objection, as I have got it, is that there must be "w+1" lines in that
sequence (i.e. from the first line with 0 up to and including the line with
w), so w is the "(w+1)-th" number... But, IMO, there is no incongruence
really, rather a relabeling: it is the "(w+1)-th" starting from "1". (To
make it explicit, I have quoted the "pre-formal" counting.)

Julio

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