In a far-away land there is a fairytale castle (Schloss Neuschwanstein in Germany, probably!) which has an infinite number of rooms. The castle rooms are numbered 1, 2, 3, ... and for each n the key to room number n +1 is locked in room number n. The princess is locked in one of the rooms, and the gallant rescuer prince has the key to room number 1. Will he be able to rescue his princess?
In essence, this problem illustrates the Principle of Mathematical Induction, which in turn is derived from one of the Peano Postulates for the natural numbers: if proposition P(1) is true, and for all natural numbers n, P(n) is true implies P(n + 1) is true, then P(n) is true for all natural numbers.
