From: Arthur Smyles
Date: Tue, 19 Jun 2007 00:47:13 -0400
Subject: [Formal] Formal Comment: NaN should be considered a number,
	not a real

NaN should be considered a number, not a real

Submitter: Arthur Smyles
Type of issue: Defect
Priority: Major
Component: arithmetic
version: 5.94

According to Section 2.4 Infinities and NaNs?

"A NaN is regarded as a real (but not rational) number whose value is so
indeterminate that it might represent any real number, including
positive or negative infinity, and might even be greater than positive
infinity or less than negative infinity."

In formal comment 11, Aubrey Jaffer correctly stated that NaN is not a
real number. But, his conclusion that a NaN is a complex number is also
incorrect. The complex numbers includes the set of all real and
imaginary numbers. NaN is neither real nor imaginary, therefore it
cannot be a value in the real or the imaginary part of a complex number,
therefore it cannot be complex. So the definition of a number is really
the set of all complex numbers and NaN.

If you treat a NaN as a number that is not complex, it will solve the
performance issues stated in formal comment 143. It will also address
formal comment 230, which will make reals conform to mathematical usage.
It will also conform with IEEE-754.

In conclusion this section should read:

A NaN is regarded as a number that is not complex.


RESPONSE:

While this position is consistent, it is often useful to compute with
complex numbers that have NaN components.  Therefore, the suggestion
has not been adopted.