
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?
Interested adult
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:
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:
Cheers,
Penny
