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Imagine a line. Imagine that line divided into equal segments. I now place a pin in the middle segment. Now I’m going to start moving this pin. Where I move it to depends on the flip of a fair coin; heads I move it left, tails I move it right. That’s the setup. Now the question: what is the probability that the pin will visit a particular segment? The answer is that, given enough coin tosses, whichever segment is selected the pin will visit it with certainty, that is the probability equals one. This probability is the first number in this series of interest. The the next number in the series, also a one.

This second number is derived from the same problem as the first with the difference that we are no longer dealing with a line, but a plane divided into equal sized square segments. Instead of a coin we randomly pick a direction to move in. Pick a starting point on a flat surface. Pick an end point. The probability that a pin, moving randomly, will eventually reach the chosen end-segment is one. No matter which end-segment you pick. Another way of putting this is that a pin moving randomly will eventually visit every single segment possible. This result is the same as for the line.