Stop being so irrational | James Howard Stop being so irrational | James Howard

James Howard A Mathematician, a Different Kind of Mathematician, and a Statistician

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Stop being so irrational

I am convinced if you study mathematics long enough, you will eventually discover something unsettling. For me, this moment came in real analysis. This morning, a friend posted on Facebook, that her five-year old son asked, “Why do numbers never end?” I gave the stock answer about countable infinity. And someone else posted a video about Hilbert’s infinite hotel:


I never found the hotel terribly troubling, but it reminds me of something else. And down the rabbit whole we go. Let’s start by establishing 4 propositions:


This always bothered me. I was never able to reconcile, in my head, these four points. I kind of felt like if the density of rationals matched the density of irrationals, then if one is countable so is the other. Ahh, I eventually gave up and did statistics, instead.

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