It's right twice a day. The number of times it's wrong is an infinite number. (between any 2 moments of time there is an infinite no. of moments, just as with numbers)
How far do you want to take this, Hugh? Most people only care to see the time in hours and minutes. Seconds? There are 60,000 Milliseconds in a minute, 60,000,000 Microseconds in a minute, and 60,000,000,000 Nanoseconds in a minute. Do we care to differentiate between succeeding Milliseconds, Microseconds, and Nanoseconds? How about Picoseconds? That's a Trillionth of a second, man!
What is really germane to our lives is that there is no such thing as 12:00AM or 12:00PM. Any street signs using either of those as a reference (rather than "noon" or "midnight) is unenforceable.
The phrase " stopped clock " (also " broken clock " or " sudden outbreak of common sense ") comes from the proverb "even a stopped clock is right twice a day", thus implying that even cranks, denialists, or conspiracy theorists that are literally wrong at every other time of the day can theoretically be correct once in a while especially in spite of their bad reasoning.
A Stopped Clock is WRONG 1438 times a day! that is the view of a pessimist An optimist says it is right twice a day
Well, if you take this very far, we will get into the area of paradoxes. Have you studied Zeno's Paradox? Or, how about the old adage that one cannot ever reach a wall be going half of the distance, then half again, and so forth? Or how about the tortoise and the hare?
That reminds me of the Asymptotic curve, never reaching the theoretical contact value, as in Y=Tan X.