Re: re:derivative notation

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 18:09:42 -0500

In <1106604097.250300.240740@f14g2000cwb.googlegroups.com>, on
01/24/2005
   at 02:01 PM, whopkins@csd.uwm.edu said:

>Actually addition is more efficient in Roman numerals, since it
>involves only a combinatorial process an is, essentially, an O(1)
>process, with 0 committment to memorizing tables.

Huh? What is V plus V? You most certainly do need to memorize tables,
in order to perform required substitutions.

>The advantage of the Hindu-Arabic system was not its efficiency with
>addition (or even multiplication, per se), but that it was
>positional involving a 0. However, the assessment of this as an
>"advantage" is, in actual fact, a fallacy. It is not necessary to
>have a 0 to have a positional system. For instance, the numerals
>I,II,III,IV,V,VI,VII,VIII,IX,X suffice quite well for representing
>all positive integers.

What is the positional representation of 144 using those numerals? And
does it qualify as a Roman numeral?

>With relatively minor extension,

If pigs had wings they could fly. A "relatively minor extension" is no
longer Roman numerals.

>(a) Everything to the left of a comma is multiplied by 1000 (b)
>Everything to the left of a dash is multiplied by 10 (commas take
>precedence over dashes)

So now instead of having one "0" symbol you have two. You've succeeded
in producing a system more complicated than either Arabic or Roman
numerals. 

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Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
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