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Perhaps, this question has been answered ago but I don't aware of its existing answer. Is there any international icon or symbol for showing Contradiction or reacing a contradiction in Mathematical contexts? The same story can be seen for showing that someone reached to the end of the proof of a theorem (The tombstone symbol ∎ , Halmos).

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$\Rightarrow\Leftarrow\quad$ –  Bill Dubuque Jun 18 '12 at 20:02
I’m more familiar with a slight variant of Bill’s symbol, $\rightarrow\leftarrow$, which I’ve used for over 40 years and picked up from other people. I’ve also seen something similar to # but larger and rotated slightly clockwise, though not so often. –  Brian M. Scott Jun 18 '12 at 20:15
I usually prefer the symbol: $$\text{Contradiction}$$ –  Asaf Karagila Jun 18 '12 at 20:18
@Babak: I’ve not seen it before, though I see that it’s mentioned in the Wikipedia article that Cameron cited. –  Brian M. Scott Jun 18 '12 at 20:23
I use ↯, but I only ever use this in my working. If I am writing something up I will always use the word "contradiction" somewhere, and after reading this thread I believe all of you will understand why... –  user1729 Jun 19 '12 at 9:19

5 Answers 5

up vote 14 down vote accepted

Different sources use different symbols (if they use symbols at all). I've seen $\Rightarrow\Leftarrow$ most often. For some others, see "Symbolic Representation" here.

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Thanks Cameron. –  Babak S. Jun 18 '12 at 20:14
I like the \blitza symbol (the first one listed at the link). Apparently, it is commonly used in Germany. I always think it describes the path of a small remote control plane that ends up falling. –  Andres Caicedo Jun 18 '12 at 20:42
Cute, @Andres. I hadn't seen that and I like its name. +1 –  Rick Decker Jun 19 '12 at 2:07
I always thought that was Harry Potter's scar... –  The Chaz 2.0 Jun 19 '12 at 3:43
Yes, I really like ↯ as my contradiction symbol. –  mixedmath Jun 19 '12 at 6:58

I am surprised to see that nobody has mentioned $\bot$. In logic, this is a standard symbol for a formula that is always false, and therefore represents a contradiction exactly.

In almost all logical formalisms, one has a rule of inference that allows one to deduce $p$ from $\bot$ for any $p$ at all, and it is usually possible to prove that $(p\land\lnot p)\to \bot$ and so forth.

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The symbol I've seen most commonly in mathematical logic statements is also the one which was taught to me in a class called "Discreet Mathematics;" it is something like a sideways number sign or "pound sign" (or "hashtag," as some might call it today).

Here's a picture of the symbol I'm talking about on imgur

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Some of my teachers and I use someone like (Harry Potter's scar) this $$\Lightning$$

Edit: I don't know why the latex of mse can't show it.

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Probably because you are using a custom symbol, or one which appear in a less-standard package. –  Asaf Karagila Feb 17 '13 at 0:55
Also had a professor who always used this. –  dreamer Jul 8 '14 at 17:49

One that all of my professors back in my college days used was "X" with each stroke looking like an axe.

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