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

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 JT Posts: 1,388 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 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 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???
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> >
>
> > But what about bijective ternary below, why would it need zero?
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> >
>
> > BASE 3 BELOW
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> > Dec = NyaNTern=StandardTern
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> >
>
> > 1 =1 01
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> > 2 =2 02
>
>
>
> [snip]
>
>
>

> > 21 =133 9+9+3 210
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> >
>
> > Why would this encoding scheme need 0?
>
>
>
> Look at the set that federation2005 is discussing:
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> N = {0, 1, 2, 3, ...}
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>
>
> Your system does not include a representation for 0.
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>
>
> If you don't care about 0, that's fine. But, then you're not
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> 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
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> >> 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
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> and 10.
>
> --
>
> Michael F. Stemper
>
> No animals were harmed in the composition of this message.

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