Counting to Infinity (Part I)

13 July 2009

People have always had a great curiosity about the infinite. I think this is because infinity represents a palpable break between our mind and our experience. You probably don’t have much difficulty imagining an infinite row of apples, but you’ve never seen one and you never will. Among the religious and spiritual, it is not unusual to identify the infinite with the divine. A great triumph of mathematical thinking, I feel, is the fact that it enables us to actually talk meaningfully about infinite things.

When people find out that I am at a mathematician, sometimes they will ask me questions. This is very interesting for me, because I get some insight into what sort of mathematical things nonmathematicians think about. A large percentage of those questions involve infinity in some way. Two popular ones are ‘Can you count to infinity?” or “Are there different kinds of infinity?” The former question strikes me as rather Zen, hence its inclusion as the title of this article. Today we’ll give at least one answer to the latter question.

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