The claim doesn't hold. Half-open intervals appear in important places. That happens mainly because the family of finite unions of half-open intervals is closed

The claim doesn't hold. Half-open intervals appear in important places. That happens mainly because the family of finite unions of half-open intervals is closed under complement (that is, they form a semi-ring; this is unrelated to the "ring" concept in abstract algebra). In measure theory, one form of the Carathéodory extension theorem [0] says that you can uniquely extend a measure on a semi-ring to an actual measure (defined on a sigma-algebra). The equivalent statement in probability theory says that a probability is uniquely determined by its cumulative distribution function, which are sometimes nicer to take limits of. You can also get a probability from a cumulative distribution function, provided your function is right-continuous [1] (which is directly related to half-open intervals). For more examples of half-open intervals in probability, you can look at stochastic processes. See, for example, càdlàgs [2] and Skorohod spaces; they capture the notion that processes that "decide to jump" (think of Markov chains changing states if you like) are right-continuous. IMO, half-open intervals are just nicer whenever you have to union them or intersect them, and are no worse in other aspects when compared to closed intervals. Also, I think the author makes a big cultural blunder when he dismisses "mathematical aesthetics" as a valid reason. A significant number of mathematicians think of elegance as the ultimate goal in mathematics; as Hardy famously said, "There is no permanent place in the world for ugly mathematics". [0] http://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_extension_theorem http://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_extension... [1] Well, we also need the obvious conditions: Correct limits at infinity and monotonicity. [2] http://en.wikipedia.org/wiki/C%C3%A0dl%C3%A0g http://en.wikipedia.org/wiki/C%C3%A0dl%C3%A0g