At 08:09 AM 10/17/03 -0600, Steven Montgomery wrote:
Can one of you mathematical types out there explain the mathematical terms, "positional" and "juxtapositional" to me? The quote comes from an article entitled, "Doing Business in Babylon," as found in the latest BYU magazine (See it online at: http://magazine.byu.edu/article.tpl?num=44-Fa03). Here is the quote:

<Quote>
Babylon seems to be the only civilization in ancient times that used a positional system, where the value of a number was determined by its position and not its juxtaposition. Even the Roman system is juxtapositional.
</Quote>



I can't get the page to come up, but here's a quick answer:


In our system, the value of a number is determined by its position, as "1", "10", "100", "1000" all represent different values, depending on the position of the "1" relative to the (understood) decimal point.

In Roman numerals, "I" always represents "1", "V" always represents "5", etc. One could conceivably put the letters that make up the representation of a particular number in Roman numerals in almost any order, so "position" is not important, except combinations like for "IV" for "4", IX" for "9", "XL" for "40", etc., where the juxtaposition of a smaller numeral to the left represents a decrement of the numeral on the right.

Clear as mud?



-- Ronn! :)

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