Subject: number systems quandary
Date: Mon, 5 Oct 1998 19:01:55 -0400

Hi,
What other number system are there besides the real number system and the complex number system?
thanks
frans

Hi
We have all learned how to count since early childhood, in fact we take most of what we do in arithmetic for granted. However, it is important to realize how our number system works, to understand its properties, and in fact to look at other possible number systems. The system that we use is called base 10 arithmetic and seems natural to us, quite possibly because of our 10 fingers. It really is not so obvious or natural. Many societies have used different bases other than 10. For an interesting historic look at such topics in the Babylonian and Egyptian cultures check out Babylonian and Egyptian mathematics. Also of interest are these sites on mathematical symbols and words: Earliest Uses of Various Mathematical Symbols and Earliest Known Uses of Some of the Words of Mathematics.
A nice example of a number system other than our base 10 system that involves different symbols and incorporates different base arithmetic is the Roman system. The symbols used are:
 1 5 10 50 100 500 1000 I V X L C D M
Further intricacies of the system are the way in which the Roman numbers are written using combinations of these symbols. The numbers 1,2, and 3 are simply I, II, III but for 4, rather than use IIII, the symbol IV is typically used, the I preceding the V denoting subtraction. Similarly we use IX for 9, XC for 90, etc. while XI and CX represent 11 and 110 respectively. For example, 1999 may be written as MDCCCCLXXXXVIIII, or, in shorter form, as MCMXCIX.

How would we add or multiply in this system? The same basic ideas that we use in other bases apply -- we will take a column for I's, V's, X's, L's, C's, etc. but the nature of the Roman system incorporates both base 2 and base 5 arithmetic -- we only need 2 V's to make an X, 2 L's to make a C, etc., but we need 5 I's to make a V, 5 X's to make an L, and so on. Thus,
 M D CC L XXX V II D CCC XX IIII + CC L XXX V II ______________________ MM D CCC L XXXX V III

in our way of thinking:
 1787 824 + 287 _____ 2898
Cheers,
Penny

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