Not A Number in IEEE Math

[Andrew P. Mullhaupt]

In article <1990Feb19.172558.29696 at gpu.utcs.utoronto.ca>, sarathy at gpu.utcs.utoronto.ca (Rajiv Sarathy) writes:
> As long as only very, VERY, large numbers (positive or negative) are defined
> to be NaNs (ie. not results of division by zero, and other silly things), then
> the above behaviour makes sense.
> 
> 	Mathematically:
> 
> 		lim    __n__ = 1.0	and     lim   0.0 * n = 0.0
> 	       n->inf    n		       n->inf
> 
> 	where inf is +/- infinity.

I would not be very convinced by this argument that (infinity/infinity)
should be taken to be 1.0, (similarly for the other). There are lots
of limits which are of the form (infinity / infinity) and they can have
any value you like. To wit:

                 n
      lim     -------  =  C 
     n->inf   csc C/n

covers all complex numbers C other than C=0, and a limit of that kind
is easy to find:

                 n
      lim      -----  =  0.
     n->inf       2
                 n

Needless to say, there are limits of the form (infinity/infinity) which
grow without bound, (these are sometimes said to have the value +infinity)
and just as well such limits can oscillate finitely or infinitely. Perhaps
the most reasonable thing to say about (infinity/infinity) without knowledge
of the limit it represents is that it is 'Not Necessarily a Number'.

Later,
Andrew Mullhaupt