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#### 6.6.2.1 Scheme’s Numerical “Tower”

Scheme’s numerical “tower” consists of the following categories of numbers:

*integers*Whole numbers, positive or negative; e.g. –5, 0, 18.

*rationals*The set of numbers that can be expressed as

where`p`/`q``p`and`q`are integers; e.g.*9/16*works, but pi (an irrational number) doesn’t. These include integers ().`n`/1*real numbers*The set of numbers that describes all possible positions along a one-dimensional line. This includes rationals as well as irrational numbers.

*complex numbers*The set of numbers that describes all possible positions in a two dimensional space. This includes real as well as imaginary numbers (

, where`a`+`b`i`a`is the*real part*,`b`is the*imaginary part*, and*i*is the square root of -1.)

It is called a tower because each category “sits on” the one that follows it, in the sense that every integer is also a rational, every rational is also real, and every real number is also a complex number (but with zero imaginary part).

In addition to the classification into integers, rationals, reals and
complex numbers, Scheme also distinguishes between whether a number is
represented exactly or not. For example, the result of
*2*sin(pi/4)* is exactly *2^(1/2)*, but Guile
can represent neither *pi/4* nor *2^(1/2)* exactly.
Instead, it stores an inexact approximation, using the C type
`double`

.

Guile can represent exact rationals of any magnitude, inexact
rationals that fit into a C `double`

, and inexact complex numbers
with `double`

real and imaginary parts.

The `number?`

predicate may be applied to any Scheme value to
discover whether the value is any of the supported numerical types.

- Scheme Procedure:
**number?***obj* - C Function:
**scm_number_p***(obj)* Return

`#t`

if`obj`is any kind of number, else`#f`

.

For example:

(number? 3) ⇒ #t (number? "hello there!") ⇒ #f (define pi 3.141592654) (number? pi) ⇒ #t

The next few subsections document each of Guile’s numerical data types in detail.

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