Virgil
Posts:
4,661
Registered:
1/6/11
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Re: Which naturals better?
Posted:
Feb 4, 2013 3:17 AM
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In article
<086315b9-274b-4e88-a43a-c8bc9ab230e4@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.
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