Numbers are basic to just about any computation. They're used for array indexes, temperatures, salaries, and an infinite variety of things. Yet they're not as simple as they seem. With floating-point numbers, how accurate is accurate? With random numbers, how random is random? With strings that should contain a number, what actually constitutes a number?.
It is important to distinguish between the mathematical numbers, the
Scheme numbers that attempt to model them, the machine representations
used to implement the Scheme numbers, and notations used to write numbers. We uses the types number, complex, real, rational, and integer to refer to both mathematical numbers and Scheme numbers. Machine representations such as fixed point
and floating point are referred to by names such as fixnum and flonum.
Scheme's numerical operations treat numbers as abstract data, as independent of
their representation as possible. Although an implementation of Scheme may use fixnum, flonum, and perhaps other representations for numbers, this should not be apparent to a casual programmer writing simple programs.
Scheme numbers are either exact or inexact. An operation may, however, return an exact result if it can prove that the value of the result is unaffected by the inexactness of its arguments. For example, multiplication of any number by an exact zero may produce an exact zero result, even if the other argument is inexact.
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