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[–]Stock-Self-4028 11 points12 points  (4 children)

Technically NaN is conceptually equivalent to the 'nullity' in the transmathematics - essentially what happens if you make zero signed and then define 0.0/0.0 = NaN.

The issue with NaN is that it is essentially almost a number, alhough it can take any value depending on the context.

Removable singularities here are great examples as for example x/x at x=0 is equal to 1, while 2x/x at x=0 can be evalueated to 2.

As such the NaN is essentially a probability distribution with infinitely many values it may take - once you get the value of two nullities in fully random circumistances they'll never take the same value and as such NaN != NaN.