Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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
up vote 13 down vote accepted

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 $S$.

In general: if you're confused, ask the person using it what they mean. And as GEdgar points out below, when you yourself use such symbols, be sure to explain what they mean at the outset.

share|cite|improve this answer
So the moral is: Don't use sign # for either of those, except perhaps in your private notes. Or when you are standing there speaking the full meaning as you write it. – GEdgar Nov 20 '11 at 21:40
For those who were as confused as I was that the hash sign # is also called the pound sign, here's an explanation. I suspect I'm not the only one who thought the pound sign would mean £. – t.b. Nov 20 '11 at 21:48
@t.b. I'd heard the names "hash sign" and "number sign" before, but I wasn't aware that in fact these were the dominant ones outside the U.S. I will keep that in mind! :) – Zev Chonoles Nov 20 '11 at 21:57
"or, try what Paul Sally does!… instead of the box, he uses a picture of himself smoking a cigar." - quoting @Eugene Bulkin from :) – Srivatsan Nov 21 '11 at 3:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.