The intuition would be something like this: half the members of the former are missing from the latter, so the former must be "twice as large" as the latter. Or perhaps it's something like this: the set of odd positive integers {1,3,5,7,9,...} is the same size as the set of even numbers {0,2,4,6,8,...}. Throw the two sets together, and you get the set {0,1,2,3,4,...}, which must "therefore" be twice as big as either of the other two.
But please remember that this path leads to perdition!
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P.S. Usage is not absolutely uniform. But I've been following one of the more standard conventions -- the one that holds the numbers 1, 2, 3, 4, 5, ... (but not 0) to be the integers (more specifically in this case, the positive integers), and the numbers 0, 1, 2, 3, 4, 5, ... to be the natural numbers. So I wouldn't call your sets {0,1,2,3,4,...} and {0,2,4,6,8,...} sets of integers. But I certainly understand what you say.
This message has been edited by Wisdom7491 on Apr 28, 2005 4:19 PM