next up previous notation contents
Next: 2.5.3 Rounding Up: 2.5 Floating Point Previous: 2.5.1 Infinity

2.5.2 NAN

Another number allowed for by computer implementations is tex2html_wrap_inline32389 . When a module implementing an operator is invoked with values for which the operator is not defined the module will return tex2html_wrap_inline32389 . For example:

math6267

since floating point is an abstraction of real numbers rather than complex numbers. tex2html_wrap_inline32389 is referred to as a NAN (not-a-number) and is a member of tex2html_wrap_inline32371 .

The NAN is not crucial to our development of number systems since it is essentially a crutch to allow for detection of exceptional conditions after they occur. They do allow for compact computer routines. Interval arithmetic routines will detect upcoming exceptional conditions before they result in an application of an operator where it is not properly defined.

The NAN causes further erosion of the comparison operators. Any comparison involving a NAN is false; the NAN is an unordered number. Every pair (x,y) of floating point numbers is ordered in one of three ways unless x or y is tex2html_wrap_inline32389 , tex2html_wrap_inline32405 , or tex2html_wrap_inline32407 .

next up previous notation contents
Next: 2.5.3 Rounding Up: 2.5 Floating Point Previous: 2.5.1 Infinity
Jeff TupperMarch 1996