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Topic: A finite set of all naturals
Replies: 32   Last Post: Aug 15, 2013 4:07 PM

 Messages: [ Previous | Next ]
 Ben Bacarisse Posts: 1,972 Registered: 7/4/07
Re: A finite set of all naturals
Posted: Aug 13, 2013 12:19 PM

Nam Nguyen <namducnguyen@shaw.ca> writes:
<snip>
>>>> Ben Bacarisse wrote: (quoting Nam)
<snip>
>>>>> Def-03a: even1(x) <-> Ey[x=y+y]
>>>>> Def-03b: even2(x) <-> Ey[x=2*y]
>>>>> Def-03c: even(x) <-> (even1(x) \/ even2(x))

<snip>
> ... _an odd number can not be defined without addition_ while
> an even number can (as per Def-03b above).

odd(x) <-> ~Ey[x=2*y]

In what sense does your definition of even2 avoid addition, where this
one of odd does not?

Personally, I'd say that both this and Def-03b use addition since
multiplication in PA is usually defined using addition, but my
view of what "without addition" means is not the issue here.

<snip>
--
Ben.

Date Subject Author
8/12/13 Ben Bacarisse
8/12/13 Peter Percival
8/12/13 fom
8/12/13 Ben Bacarisse
8/12/13 namducnguyen
8/12/13 namducnguyen
8/12/13 antani
8/12/13 namducnguyen
8/13/13 Marshall
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/15/13 namducnguyen
8/15/13 Virgil
8/15/13 namducnguyen
8/15/13 antani
8/13/13 antani
8/13/13 Peter Percival
8/13/13 Ben Bacarisse
8/13/13 namducnguyen
8/14/13 Peter Percival
8/14/13 Shmuel (Seymour J.) Metz