In this game, any side can choose to play to a tie and be successful at that. The original question is not about math so much as it is about game theory. If the algorithm is to actively confuse you about what the algorithm is, things might get really interesting.If the algorithm seems to be picking some number at random, writhing it to Nth place where N > 1 and then writing second number differing by 1 in the last place, then it is largely irrelevant what to declare.If the algorithm seems to be uncorelated random uniform distribution and the number seen is less than 0.5, than declare it to be the least of the two.One can observe the way the game is played and try to model the algorithm used to choose the numbers and use that model when making a decision. How can one expect to be correct more than half the times you play Number you see is the biggest or smallest of the two.īut one can see the number before making a statement.
You have to select one of the sheets randomly and declare whether the In the beginning, nothing is known about the choosing-and-writing process other than the range of possible values.
Though bare sets have counterintuitive results with sets containing equally large copies of themselves, these don't necessarily translate when more structure is added. Mathematicians add more structure to sets, like probability measures $\mu$ or orders, and these fundamentally change their nature. I think, maybe, the big thing to think about here is that sets really don't have a lot of structure. Worse, not all uncountable sets have an intrinsic notion of ordering - how, for instance, do you order the set of subsets of natural numbers? The problem is not that there's no answer, but that there are many conflicting answers to that. Let $\mathbb$ which is not uncountably infinite. Uncountable has the following interesting property: The set of real numbers between (0, 1) is known as an Uncountably Infinite Set My answer was that it was impossible, as the probability should always be 50% for the following reason: HowĬan one expect to be correct more than half the times you play this Whether the number you see is the biggest or smallest of the two. You have to select one of the sheets randomly and declare Two distinct real numbers between 0 and 1 are written on two sheets of I attempted to answer this question on Quora, and was told that I am thinking about the problem incorrectly.