How to prove something that doesn't stand:

Lets take a simple case.. We can prove to you that there is no such thing as a surprise midterm, no matter how hard a teacher may try, the students will expect it... Well, actually we'll only prove this for one week (for the sake of brevity).. If you want to prove this for an entire year (lets say), use induction/recursion to adjust this reasoning to the specific time frame.. Ok, here goes.. lets have a look at a little story...

Teacher:   Hello students, before I start the lesson today, I'd like to inform you that sometime next week, we'll be having a surprise midterm..       Student:   Sir.. ..there is absolutely no way you can give us a surprise midterm next week!       Teacher:   Oh really :) How come? why is that so?.. tell me..       Student:   The reason is quite simple.. let me put it this way...   If you decide to give us the midterm on Friday.. and the days go by.. and its Thursday.. then we will know the midterm will be on Friday.. 'cause there will be no other day left in the week.. so it will not be a surprise 'cause we will be expecting it.. So you cannot give us a surprise midterm on Friday   If you decide to give us the midterm on Thursday.. and the days go by.. and its Wednesday.. then we will know the midterm will be on Thursday.. 'cause there will be no other day left in the week (since Friday will not be a surprise).. so it will not be a surprise 'cause we will be expecting it.. So you cannot give us a surprise midterm on Thursday   If you decide to give us the midterm on Wednesday.. and the days go by.. and its Tuesday.. then we will know the midterm will be on Wednesday.. 'cause there will be no other day left in the week (since we've shown that a midterm on Friday or Thursday, will not be a surprise midterm).. so it will not be a surprise 'cause we will be expecting it.. So you cannot give us a surprise midterm on Wednesday   If you decide to give us the midterm on Tuesday.. and its Monday.. then we will know the midterm will be on Tuesday.. 'cause there will be no other day left in the week (since we've shown that a midterm on Friday, Thursday or Wednesday will not be a surprise midterm).. so it will not be a surprise 'cause we will be expecting it.. So you cannot give us a surprise midterm on Tuesday   If you decide to give us the midterm on Monday.. then we will know the midterm will be on Monday.. 'cause there will be no other day left in the week (since we've shown that you cannot give us a surprise midterm on Friday, Thursday, Wednesday or Tuesday).. so it will not be a surprise 'cause we will be expecting it.. So you cannot give us a surprise midterm on Monday   ..so you cannot give us a surprise midterm next week, cause we've shown that a midterm on any day (Friday,Thursday,Wednesday,Tuesday,Monday).. will not be a surprise midterm!       Teacher:   umm.. I guess you are right.. but you're having that midterm.. anyway! :)       Student:   Oh well.. I guess it was a good try :(

I guess a story is worth more than a thousand words ..if it IS more than a thousand words that is :) anyway, this story clearly demonstrates how one could prove something that doesn't stand (surprise midterms do exist unfortunately)..