In Math 683 you will be introduced to the nature of theoretical mathematics. Topics include logic, sets, concept formulation, and methods of proof. If Jones is transferred to North Africa, then Smith is going to a new post. Smith is not going to a new post. Therefore, Brown will be appointed undersecretary.
All people have the same eye color - a proof by mathematical induction.
Then every set of n people have the same eye color. By the induction hypothesis, the remaining n have the same eye color. Again by the induction hypothesis, the n people in the room have the same eye color. Since Betty's eye color matched the others before, when she reenters the room, her eye color will still match the others. Find the fallacy in this argument.