A professor tells his class that he will give them a surprise examination sometime next week.
For our purposes, an examination is considered a "surprise" if on that day, the class is not 100% sure that they will get an examination. (If they only suspect it, the examination can still be a surprise.)
Having given the class this warning, is it still possible for the professor to give them a surprise examination next week? (Assume that he will not give them an exam if it will not be a surprise.)
(In reply to
You guys are forgetting something... by Bruno)
You wrote, "If we eliminate Friday by this process and we want to eliminate Thursday the same way, we must now include Friday back in the days that the test is possible."
No, Bruno, we must not include Friday back in the possible days. We have already eliminated it. And we are now examining Thursday. This is an example of the notion of recursivity.
Since I don't wish to repeat myself, please look here or here for the explanation of your preference.
The paradox comes from the "fact" that we've eliminated all the possible days, and therefore we don't expect it on any day, and when it occur we are surprised.
Hope this clears it up for ya. :)
re: You guys are forgetting something...
