Is a broken clock right twice a day?

If the bad clock runs wrong by a factor $k\in\mathbb{R}_+$, for example $k=2$ means that it runs at double speed, then the first time the bad clock is correct is $(12\ \mbox{hours})/|1 - k|$ after the start (where the two clocks agree). By choosing $k$ very close to $1$, you can make that time span as long as you desire (so no, there's not an upper bound).

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Periodic Functions

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