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Topic: A finite set of all naturals
Replies: 44   Last Post: Aug 30, 2013 6:59 AM

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 fom Posts: 1,719 Registered: 12/4/12
Re: A finite set of all naturals
Posted: Aug 29, 2013 5:48 AM

On 8/29/2013 4:17 AM, Peter Percival wrote:
> Nam Nguyen wrote:
>

>>
>> As well as _could_ be denoted by S0, in the language of arithmetic
>> L(0,<,S,+,*).
>>
>> Note that 'S0' is _not_ a language individual constant symbol of
>> L(0,<,S,+,*) hence it can only be a defined symbol.

>
> You are using language in a very non-standard way. 'S0' is neither a
> constant symbol nor a defined symbol; it isn't a symbols at all. Rather
> it's a string of two symbols, one a function symbol and the other an
> individual constant. It looks to me like a term, but below you seem to
> be making a distinction between S0 and S(0).

It would normally be considered a term.

Based on the usage, however, Nam uses
parentheses for term generation. So,
the syntactic concatenation could be
taken as an implicitly defined symbolic
constant.

Just another example of difficulty and
confusion with respect to some of Nam's
statements. As you are quite aware, typical
presentations of Peano arithmetic simplify
the syntax of those terms by dropping the
parentheses. Since one might see a term
such as

S(S0 + SS0)

in the very same presentations, one could say
that Nam is making the correct rigorous distinction.

Perhaps something has been clarified here.
Probably not.

Date Subject Author
8/26/13 Ben Bacarisse
8/26/13 namducnguyen
8/26/13 quasi
8/27/13 Virgil
8/27/13 namducnguyen
8/27/13 quasi
8/27/13 quasi
8/27/13 quasi
8/27/13 namducnguyen
8/27/13 quasi
8/27/13 namducnguyen
8/27/13 quasi
8/27/13 namducnguyen
8/27/13 quasi
8/27/13 quasi
8/27/13 namducnguyen
8/27/13 quasi
8/27/13 namducnguyen
8/27/13 quasi
8/27/13 Shmuel (Seymour J.) Metz
8/27/13 namducnguyen
8/28/13 Peter Percival
8/28/13 Shmuel (Seymour J.) Metz
8/28/13 Peter Percival
8/28/13 Peter Percival
8/28/13 namducnguyen
8/29/13 Shmuel (Seymour J.) Metz
8/29/13 namducnguyen
8/28/13 fom
8/28/13 namducnguyen
8/29/13 Peter Percival
8/29/13 fom
8/29/13 namducnguyen
8/30/13 Peter Percival
8/28/13 Shmuel (Seymour J.) Metz
8/28/13 namducnguyen
8/29/13 Shmuel (Seymour J.) Metz
8/27/13 quasi
8/27/13 Peter Percival
8/27/13 Peter Percival
8/27/13 Peter Percival
8/26/13 Ben Bacarisse