# Re: is NaN a number?

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``` | Date: Thu, 19 May 2005 11:18:44 +0900
| From: Alex Shinn <alexshinn@xxxxxxxxx>
|
| Is the following a typo?
|
|   (complex? 0/0)                         ==>  #t
|   (real? 0/0)                            ==>  #f
|
| One would assume that
|
|   (complex? x)    ->    (real? (real-part x))
|
| Moreover, since 0/0 is by definition "Not a Number" it seems natural that
|
|   (number? 0/0)    ==>   #f

Thus far in SRFI-70, 0/0 is not a real number, but it is a number.

0/0 is contagious through all numerical operations (which don't signal
errors).  Having it be a number allows it to be an argument to those
operations.  Alternatively, an implementation could make 0/0
non-numeric and extend numeric operations to accept it or not.  But
extending STRING->NUMBER and NUMBER->STRING to deal with a type other
than numbers is awkward.

0/0's contagion should make:

(real-part 0/0)                     ==> 0/0
(imag-part 0/0)                     ==> 0/0
(magnitude 0/0)                     ==> 0/0
(angle 0/0)                         ==> 0/0

which requires modification of the z = x1 + i x2 = x3^(i x4) rule if
0/0 is complex.

Because 0/0 is an optional feature, leaving to the implementation the
choice of values for (complex? 0/0) and (number? 0/0) complicates
portable code dealing with it.  So I will change SRFI-70 so that:

(number? 0/0)                       ==>  #t
(complex? 0/0)                      ==>  #f

```