My friends, I want to tell you that you’re in extremely good company.
My post making fun of Mitt Romney’s pretentious misuse of the terms “null set” and “non sequitur” contained a careless error, which is an especially bad thing to have in a post making fun of someone else’s mistakes. I wrote that that the null set can be written either { } or { ø }. That’s wrong, of course: { ø } isn’t the null set, it’s the set containing the null set as its only member. (Think of the difference between the statement “The room was empty” and “The room contained only an empty box.”) The null set can be written either as { } or as ø .
[As it happens, though, { ø } symbolizes something important. In Peano’s work on the foundations of arithmetic, { } or ø, the null set itself, exemplifies the number zero: it has no elements. { ø }, the set containing the null set, exemplifies the number one, because it has a single element. Similarly, { ø, {ø} }the set containing ø and {ø}, has two elements and exemplifies the number two. Continuing in this way we can generate the sequence of natural numbers.]
What’s striking is that this simple error generated no fewer than nine email corrections, all of them polite. That’s about 8.5 more email responses than the average post draws. So in reading this blog you have joined a group both erudite and generous of spirit.
Try not to let it go to your head.