[justin_vanw]

It certainly isn't ironic nor is it a breakdown, the pigeonhole principle is stated on finite number of containers and a finite number of pigeons.

However, if you just arbitrarily change it around, you may well find that the new statement you just generated is not true any more, if it even makes sense at all.

[im3w1l]

It's ironic from my point of view because the article cautions against hasty generalizations, and that was a generalization I implicitly did upon first hearing about Hilbert's paradox of the Grand Hotel.