[adamzochowski]

This looks very much like NULLs in the SQL world.

A null (and NaN) is like an unknown. One can't compare unknowns because they are exactly that, unknown.

Let's construct a language that on division on zero returns unknowns.

   a =  5 / 0;
   b = 10 / 0;

Now, both a and b are set to unknown state. If one were to compare a to b, should the expectation be that they hold same value?

I wish all languages would have nullability like SQL does. Where a great care has to be given to deal with nullable data, lest nulls nullify everything.

[malkia]

In some languages, a, b would be +Infinity. On top of my head I can't remember whether +Infity != +Infinity (have to write a test and see). For NaN's definitely.

[tikhonj]

One of those languages is JavaScript, so--assuming your browser supports JavaScript--you do have somewhere to test it :P.

The answer is that 5 / 0 is Infinity and (5 / 0) == (5 / 0), so it's all good :). Now, 0 / 0 is NaN and (0 / 0) != (0 / 0).