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Third attempt

Posted By: Jason Lee
Date: Saturday, 2 March 2013, at 10:58 p.m.

In Response To: Third attempt (Bob koca)

So is a game that is not completed because it has an infinite number of moves really a complete game?

I'm thinking of this as a mathematical problem, not necessarily a realization of something that happens.

If I tell you to consider the sequence 1, 1/2, 1/3, 1/4, etc., and say something to the effect of, "This sequence tends to zero." This has a precise mathematical statement that doesn't invoke any weirdness with infinity. I don't need you to be able to list those terms "forever."

Here's a mathematical abstraction of a an infinite backgammon game: it's an infinite sequence of positions, where the first term of the sequence is the opening position, and every subsequent term is reachable from the previous position with a backgammon move for some roll of the dice, and neither player ever bears off all of their checkers.

JLee

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