Virgil
Posts:
7,021
Registered:
1/6/11


Re: Which naturals better?
Posted:
Feb 4, 2013 3:17 AM


In article <086315b9274b4e88a43ac8bc9ab230e4@n2g2000yqg.googlegroups.com>, JT <jonas.thornvall@gmail.com> wrote:
> Building new natural numbers without zero using NyaN, in any base, > this will have affects upon computational theory? The NyaN principle > is general work for all bases. > (Base 3) > (NyaN) base 3 Standard naturals base 3 > 1 = 1 01 > 2 = 2 02 > 3 = 3 10 > 4 = 11 =3+1 11 > 5 = 12 =3+2 12 > 6 = 13 =3+3 20 > 7 = 21 =6+1 21 > 8 = 22 =6+2 22 > 9 = 23 =6+3 100 > 10 = 31 =9+1 101 > 11 = 32 =9+2 102 > 12 = 33 =9+3 110 > 13 = 111 =9+3+1 111 > 14 = 112 =9+3+2 112 > 15 = 113 =9+3+3 120 > 16 = 121 =9+6+1 121 > 17 = 122 =9+6+2 122 > 18 = 123 =9+6+3 200 > 19 = 131 =9+9+1 201 > 20 = 132 =9+9+2 202 > 21 =133 =9+9+3 210
The problem being that in this NyaN system there is no way to represent zero as a numeral, and zero is more and more these days regarded as natural number, since it is certainly the cardinality of a finite set, as are all 'other' natural numbers. 

