# I'm confused: does # mean Q.E.D. or contradiction?

Last week one teacher used the pound sign # for implying that we were done proving something and a different teacher used the same for highlighting a contradiction.

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I'm from the UK, and in my experience "#" is used invariably to mean 'contradiction' (though in practice it is usually a bit larger than the standard hash symbol and more slanted) –  Daniel Freedman Nov 21 '11 at 0:07

Many symbols in math don't have a single meaning; and in fact this is not quite mathematics, but rather the use of a symbol as a shorthand, among mathematicians, for what would otherwise be an ordinary statement in one's language. One common symbol for "we are done proving this" is the tombstone (e.g. $\blacksquare$ or $\Box$), and I've even seen $\clubsuit$. I've also seen $\Rightarrow\Leftarrow$ for "this is a contradiction". So, the fact that two people use the pound (a.k.a. hash, number) sign $\#$ for these two different things is not a problem. For example, I wouldn't use $\#$ for either of those purposes, but I might use $\# S$ to denote the cardinality of the set $S$.