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Mathematics : a discrete introduction
The world of mathematics can be divided roughly into two realms: the con-
tinuous and the discrete. The difference is illustrated nicely by wristwatches.
Continuous mathematics corresponds to analog watches-the kind with separate
hour, minute, and second hands. The hands move smoothly over time. From an ana-
log watch perspective, between 12:02 P.M. and 12:03 P.M. there are infinitely many
possible different times as the second hand sweeps around the watch face. Contin-
uous mathematics studies concepts that are infinite in scope, in which one object
blends smoothly into the next. The real-number system lies at the core of con-
tinuous mathematics, and-just as on the watch-between any two real numbers,
there is an infinity of real numbers. Continuous mathematics provides excellent
models and tools for analyzing real-word phenomena that change smoothly over
time, including the motion of planets around the sun and the flow of blood through
the body.
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