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Chapter 3
Rational and
Irrational Numbers
3.1 APPEARANCE OF FRACTIONS
Counting is the simplest and most fundamental operation using numbers.
However, just counting was insucient and inconvenient for people even
in ancient civilizations. People at some early stage of their civilizations
realized that arithmetic operations such as addition, subtraction, multi-
plication, and division were necessary and very important. It is probably
more than 4000 years ago that people in Egypt, Mesopotamia, and other
ancient civilized regions could already manipulate arithmetic operations
using their number systems, although it is dicult to specify when a ...