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Topic: Is there a name for this notation?
Replies: 8   Last Post: Oct 9, 2011 9:17 PM

 Messages: [ Previous | Next ]
 Kaba Posts: 289 Registered: 5/23/11
Re: Is there a name for this notation?
Posted: Oct 9, 2011 8:52 AM

A N Niel wrote:
> In article <4e919166\$0\$29981\$c3e8da3\$5496439d@news.astraweb.com>,
> Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:
>

> >[...]>
> > You'd need either a digit for 100, or some notation for grouping digits.
> > E.g.:
> >
> > 2^10 => A
> > 2^11 => B
> > 2^12 => C
> > ...
> >
> > but since we can't realistically have an infinite number of unique symbols,
> > a grouping notation might be better:
> >
> > 2^100 + 2^50 + 2^10 + 2^2 = (100)(50)(10)2

>
> Since it is just a set anyway, maybe {100,50,10,2}

In the case of "base 2", this can be seen as a sparse form of the
traditional base-2 representation. Let I subset NN. Then the value of I
is given by

V(I) = sum_{i in I} 2^i,

i.e. the set I encodes the positions of the 1-bits, rather than giving a
"dense" tuple of coefficients where some elements might be 0. Higher
bases probably sacrifice some property, possibly uniqueness.

--
http://kaba.hilvi.org

Date Subject Author
10/8/11 Steven D'Aprano
10/9/11 William Elliot
10/9/11 Steven D'Aprano
10/9/11 A N Niel
10/9/11 Kaba
10/9/11 Kaba
10/9/11 Kaba
10/9/11 Kaba
10/9/11 Tommy Jensen