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Re: Systems of Numerals (not Numbers)
Posted:
Sep 30, 2013 5:55 PM


On 09/30/2013 04:14 PM, jonas.thornvall@gmail.com wrote: > Den måndagen den 30:e september 2013 kl. 22:24:57 UTC+2 skrev federat...@netzero.com: >> On Monday, September 30, 2013 10:57:49 AM UTC5, jonas.t...@gmail.com wrote:
>>> When i've played with constructing *zeroless* numbersystems i've come a cross terms like bijective and padic, since my formalised knowledge of math terms is null.
>> The smallest base for a numeric orthography for the natural numbers N = {0, 1, 2, 3, ... } is 2. Of >> necessity, any positional system has to either include a symbol for 0 or a representation of 0 formed >> of the other symbols. Since the base can only be positive (lest negative be represented), then 0 has >> to be a symbol. > > Really??? > > But what about bijective ternary below, why would it need zero? > > BASE 3 BELOW > Dec = NyaNTern=StandardTern > > 1 =1 01 > 2 =2 02
[snip]
> 21 =133 9+9+3 210 > > Why would this encoding scheme need 0?
Look at the set that federation2005 is discussing: N = {0, 1, 2, 3, ...}
Your system does not include a representation for 0.
If you don't care about 0, that's fine. But, then you're not representing N, you're representing the counting numbers, which were addressed in the next paragraph of federation2005's post:
>> For the counting numbers { 1, 2, 3, ... } the smallest base is 1. That >> does not require any 0. Nor does any other base. For base 10, for >> instance, the digits would have the values 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.  Michael F. Stemper No animals were harmed in the composition of this message.



