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is NaN a number?

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Is the following a typo?

  (complex? 0/0)                         ==>  #t
  (real? 0/0)                            ==>  #f

One would assume that

  (complex? x)    ->    (real? (real-part x))

Moreover, since 0/0 is by definition "Not a Number" it seems natural that

  (number? 0/0)    ==>   #f