You’re right. I Misremembered, but i checked and it is true that a bounded montonic function of the reals can have only a countable number of discontinuities. So if ROB knows our algorithm, he can select one continuous interval for all of his values to come from.
Proof of the countable nature of discontinutes given here:
You’re right. I Misremembered, but i checked and it is true that a bounded montonic function of the reals can have only a countable number of discontinuities. So if ROB knows our algorithm, he can select one continuous interval for all of his values to come from.
Proof of the countable nature of discontinutes given here:
https://math.stackexchange.com/questions/2793202/set-of-discontinuity-of-monotone-function-is-countable