This isn't precisely a paradox. But the result comes from deriving a contradiction. This is an attempt to produce a list of the real numbers which are claimed to be unlistable. I will follow the standard proof with an interesting counterexample. It suffices to limit our scope to the numbers between zero and one. The conclusion: The real numbers are NOT listable because we posited a list with all the real numbers on it and then constructed a number not on the list.