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Replies: 23   Last Post: Oct 1, 2013 3:22 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective, p-adic etc)
Posted: Sep 30, 2013 7:32 PM

> Den tisdagen den 1:e oktober 2013 kl. 00:05:18 UTC+2 skrev Virgil:
> > 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 UTC-5, jonas.t...@gmail.com
> > > > wrote:

> > > > > When i've played with constructing *zeroless* numbersystems i've come
> > > > > a
> > > > > cross terms like bijective and p-adic, 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 zero-less 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

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?
--

Date Subject Author
9/30/13 JT
9/30/13 JT
9/30/13 JT
9/30/13 FredJeffries@gmail.com
9/30/13 JT
9/30/13 Brian Q. Hutchings
9/30/13 JT
9/30/13 JT
9/30/13 Rock Brentwood
9/30/13 JT
9/30/13 Michael F. Stemper
9/30/13 JT
9/30/13 JT
9/30/13 JT
9/30/13 Virgil
9/30/13 JT
9/30/13 Virgil
9/30/13 JT
9/30/13 Virgil
10/1/13 Brian Q. Hutchings
10/1/13 Brian Q. Hutchings
10/1/13 Michael F. Stemper
10/1/13 Brian Q. Hutchings
10/1/13 Karl-Olav Nyberg