Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Virgil
Posts:
8,833
Registered:
1/6/11


Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective, padic etc)
Posted:
Sep 30, 2013 7:32 PM


> Den tisdagen den 1:e oktober 2013 kl. 00:05:18 UTC+2 skrev Virgil: > > In article <e6cbafe9d5f348b2853907ea1457ee03@googlegroups.com>, > > jonas.thornvall@gmail.com wrote: > > > Den m?ndagen 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 correct term, actually, would be systems of numerals. Numerals are > > > > not > > > > numbers, but merely symbols to denote numbers. So, technically, this is > > > > not > > > > a question of mathematics at all, but of orthography, which is a part > > > > of > > > > linguistics. > > > > Others have deal with the main question (including a Wikipedia link), > > > > but > > > > there are a few comments to be made on zeroless orthographies. > > > > In most cases (including the Wikipedia links, last I checked), there is > > > > a > > > > failure to note that the question has to be asked RELATIVE to the set > > > > that's being represented! > > > > 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 > > > 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 > > > Why would this encoding scheme need 0? > > Until you have shown us that the arithmetic of your notation is at > > lestas simple as that of standard base ten (or other bases like 2, 8 or > > 16). > > How do you add, subtract, multiply, divide, take square roots, averages, > > etc., in your notation? > > What happens when you need to subtract a number from itself? > > How do you deal with integers needing both 0 and negatives? > > And > >  > > I know my arithmetic will do just fine without zeros since i have implemented > it before.
You claim you do you do but we don't, and do not choose merely to take your word for it.
For example how do you represent 0 and negatives?
What is your alternative for decimal fractions?
E.g., how would you represent decimal fractions, like 0.01, 0.001, 0.0001, and so on, without zeros? 



