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JT
Posts:
1,299
Registered:
4/7/12


Re: Systems of Numerals (not Numbers)
Posted:
Sep 30, 2013 6:10 PM


Den måndagen den 30:e september 2013 kl. 23:55:09 UTC+2 skrev Michael F. Stemper: > On 09/30/2013 04:14 PM, jonas.thornvall@gmail.com wrote: > > > Den mï¿½ndagen 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 > Well actually here i represented the counting numbers but i intend to represent the reals using the system. > were addressed in the next paragraph of federation2005's post: > Well if he state that the set of naturals contain 0 in the definition of set, i really do not see why he has to point out the necessity of zero.
> > >> 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.



