Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
JT

Posts: 1,150
Registered: 4/7/12
Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective,
p-adic etc)

Posted: Sep 30, 2013 6:12 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
>
> > 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.


Date Subject Author
9/30/13
Read Numbersystems, bijective, p-adic etc
JT
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
JT
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
JT
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
FredJeffries@gmail.com
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
JT
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
Brian Q. Hutchings
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
JT
9/30/13
Read Re: Numbersystems, bijective, p-adic etc
JT
9/30/13
Read Systems of Numerals (not Numbers) (was: Numbersystems, bijective,
p-adic etc)
Rock Brentwood
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective,
p-adic etc)
JT
9/30/13
Read Re: Systems of Numerals (not Numbers)
Michael F. Stemper
9/30/13
Read Re: Systems of Numerals (not Numbers)
JT
9/30/13
Read Re: Systems of Numerals (not Numbers)
JT
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective,
p-adic etc)
JT
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective, p-adic etc)
Virgil
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective,
p-adic etc)
JT
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective, p-adic etc)
Virgil
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective,
p-adic etc)
JT
9/30/13
Read Re: Systems of Numerals (not Numbers) (was: Numbersystems, bijective, p-adic etc)
Virgil
10/1/13
Read base-one accounting for
Brian Q. Hutchings
10/1/13
Read the surfer's value of pi (wokrking on proof
Brian Q. Hutchings
10/1/13
Read Re: the surfer's value of pi (wokrking on proof
Michael F. Stemper
10/1/13
Read Re: the surfer's value of pi (wokrking on proof
Brian Q. Hutchings
10/1/13
Read Re: Numbersystems, bijective, p-adic etc
Karl-Olav Nyberg

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.