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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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migrated from Jun 18 '12 at 20:11

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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
up vote 17 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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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. – Andrés 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
The ↯ symbol seems to be very common : in France, my first teacher after high school, used this symbol too (since I use it unconsciously). – JBC Jun 19 '12 at 21:24

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 "Discrete Mathematics;" it is something like a sideways number sign or "pound sign" (or "hashtag," as some might call it today).

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How do you generate this symbol? – Anthony Dec 17 '15 at 23:51

Some of my teachers and I use someone like (Harry Potter's scar) this $\unicode{x21af}$ (LaTex: \unicode{x21af})

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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

The bottom and top symbols $\bot,\,\top$ respectively denote contradictions and tautologies in model theory. For example, a proof by contradiction that $\sqrt{2}\notin\mathbb{Q}$ can be rewritten as a proof that $\sqrt{2}\in\mathbb{Q}\to\bot$.

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Thanks for letting me know that. +1 – S. Snape Feb 9 at 7:39

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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