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MATH Thought for the Day!

Beckman Institute

From Paul Halmos

"My most nearly immortal contributions are an abbreviation and a typographical symbol.

I invented "iff" for "if and only if" --but I could never believe that I was really its first inventor. . . . . .

The symbol is definitely not my invention - it appeared in popular magazines (not mathematical ones) before I adopted it, but once, again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like ∎, and is used to indicate an end, usually the end of a proof. It is most frequently called the 'tombstone', but at least one generous author referred to it as the 'halmos'."

From I Want to Be a Mathematician: An Automathography,
by Paul Halmos, Springer-Verlag, 1984.

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