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Topic: Numbersystems, bijective, p-adic etc
Replies: 23   Last Post: Oct 1, 2013 3:22 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,434 Registered: 4/7/12
Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective,

Posted: Sep 30, 2013 6:12 PM

Den tisdagen den 1:e oktober 2013 kl. 00:05:18 UTC+2 skrev Virgil:
> In article <e6cbafe9-d5f3-48b2-8539-07ea1457ee03@googlegroups.com>,
>
> jonas.thornvall@gmail.com wrote:
>
>
>

> > Den m?ndagen den 30:e september 2013 kl. 22:24:57 UTC+2 skrev
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> > federat...@netzero.com:
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> > > On Monday, September 30, 2013 10:57:49 AM UTC-5, jonas.t...@gmail.com
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> > > wrote:
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> > >
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> > > > When i've played with constructing *zeroless* numbersystems i've come a
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> > > > cross terms like bijective and p-adic, since my formalised knowledge of
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> > > > math terms is null.
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> > >
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> > >
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> > >
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> > > The correct term, actually, would be systems of numerals. Numerals are not
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> > > numbers, but merely symbols to denote numbers. So, technically, this is not
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> > > a question of mathematics at all, but of orthography, which is a part of
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> > > linguistics.
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> > >
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> > >
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> > >
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> > > Others have deal with the main question (including a Wikipedia link), but
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> > > there are a few comments to be made on zero-less orthographies.
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> > >
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> > >
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> > >
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> > > In most cases (including the Wikipedia links, last I checked), there is a
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> > > failure to note that the question has to be asked RELATIVE to the set
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> > > that's being represented!
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> > >
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> > >
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> > >
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> > > The smallest base for a numeric orthography for the natural numbers N = {0,
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> > > 1, 2, 3, ... } is 2. Of necessity, any positional system has to either
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> > > include a symbol for 0 or a representation of 0 formed of the other
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> > > symbols. Since the base can only be positive (lest negative be
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> > > represented), then 0 has to be a symbol.
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> >
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> > Really???
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> >
>
> > But what about bijective ternary below, why would it need zero?
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> >
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> > BASE 3 BELOW
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> > Dec = NyaNTern=StandardTern
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> >
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> > 1 =1 01
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> > 2 =2 02
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> > 3 =3 10
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> > 4 =11 3+1 11
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> > 5 =12 3+2 12
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> > 6 =13 3+3 20
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> > 7 =21 6+1 21
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> > 8 =22 6+2 22
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> > 9 =23 6+3 100
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> > 10 =31 9+1 101
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> > 11 =32 9+2 102
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> > 12 =33 9+3 110
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> > 13 =111 9+3+1 111
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> > 14 =112 9+3+2 112
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> > 15 =113 9+3+3 120
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> > 16 =121 9+6+1 121
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> > 17 =122 9+6+2 122
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> > 18 =123 9+6+3 200
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> > 19 =131 9+9+1 201
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> > 20 =132 9+9+2 202
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> > 21 =133 9+9+3 210
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> >
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> > Why would this encoding scheme need 0?
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>
>
> Until you have shown us that the arithmetic of your notation is at
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> lestas simple as that of standard base ten (or other bases like 2, 8 or
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> 16).
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>
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> How do you add, subtract, multiply, divide, take square roots, averages,
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> etc., in your notation?
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>
>
> What happens when you need to subtract a number from itself?
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>
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> How do you deal with integers needing both 0 and negatives?
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>
>
> And
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> --

I know my arithmetic will do just fine without zeros since i have implemented it before.

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