For those of you who haven't been following Cornell professor Steven Strogatz's math columns in the NYTimes for the last couple of months, you've been out on a gem of a series. In his last and final column Strogatz shows how certain types of infinity can be larger than others. He even writes it in a way that a Hotelie can understand: While this foray into set theory and the foundations of real analysis represents his last column in the series, the good news is that Strogatz is planning on expanding the series into book form, to be published in 2012. Do I smell the 21st century version of Strunk and White?The coup de grace is Cantor's proof that some infinite sets are bigger than this. Specifically, the set of real numbers between 0 and 1 is "uncountable” -- it can't be put in one-to-one correspondence with the natural numbers. For the hospitality industry, this means that if all these real numbers show up at the reception desk and bang on the bell, there won't be enough rooms for all of them, even at the Hilbert Hotel.
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