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2010 | OriginalPaper | Buchkapitel
Infinity
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Abstract
Galileo, whose scientific activities were celebrated during the International Year of Astronomy, considered various paradoxes having to do with infinity. One of the simplest and most illustrative paradoxes concerns two sets, one of the natural numbers (1, 2, 3, …), and one of their doubles (2, 4, 6, …). We can establish a one-to-one (bijection) correspondence between the two sets: 1 corresponds to 2, 2 corresponds to 4, 3 corresponds to 6, and so on. The first set seems to contain twice as many elements as the second set, because it contains both odd and even numbers. But doesn’t the fact that we can establish a one-to-one correspondence between each number and its double indicate that each set has the same number of elements?