21 Jan
2016
21 Jan
'16
8:50 a.m.
Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly.
It's still true, though -- just vacuously so.
Do all unicorns have 1 horn (by definition) or 0 (by nonexistence)?
Yes. (And, less trivially, both of the disjunctands are also true.) Best wishes, Adam P. Goucher