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

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LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
Re: Can L(<) be the language of the naturals?
Posted: Sep 6, 2013 3:35 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"Albrecht" <albstorz@gmx.de> wrote in message
news:de62b240-ff1c-4ed3-afc8-0de4b3f89f8a@googlegroups.com...

> 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
Read Can L(<) be the language of the naturals?
Jim Burns
9/1/13
Read Re: Can L(<) be the language of the naturals?
Jim Burns
9/1/13
Read Re: Can L(<) be the language of the naturals?
David Hartley
9/1/13
Read Re: Can L(<) be the language of the naturals?
Peter Percival
9/1/13
Read Re: Can L(<) be the language of the naturals?
Virgil
9/1/13
Read Re: Can L(<) be the language of the naturals?
Peter Percival
9/1/13
Read Re: Can L(<) be the language of the naturals?
Virgil
9/2/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
Robin Chapman
9/6/13
Read Re: Can L(<) be the language of the naturals?
Tucsondrew@me.com
9/6/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/6/13
Read Re: Can L(<) be the language of the naturals?
Tucsondrew@me.com
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
Michael F. Stemper
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
FredJeffries@gmail.com
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/7/13
Read Re: Can L(<) be the language of the naturals?
FredJeffries@gmail.com
9/8/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
Robin Chapman
9/6/13
Read The decimals by Stevin
Brian Q. Hutchings
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/6/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/7/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/7/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/8/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/8/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/8/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/9/13
Read Re: Can L(<) be the language of the naturals?
LudovicoVan
9/10/13
Read Re: Can L(<) be the language of the naturals?
albrecht
9/1/13
Read Re: Can L(<) be the language of the naturals?
Jim Burns
9/2/13
Read Re: Can L(<) be the language of the naturals?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: Can L(<) be the language of the naturals?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: Can L(<) be the language of the naturals?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: Can L(<) be the language of the naturals?
Peter Percival

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