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Today's xkcd describes magic proofs. Can anyone think of some good examples of these?

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    $\begingroup$ It is generally considered to be a non-proof. Here is a list of other invalid proof techniques. $\endgroup$
    – JMoravitz
    Commented Aug 25, 2016 at 20:32
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    $\begingroup$ @JMoravitz That depends on what exactly "it" is. $\endgroup$ Commented Aug 25, 2016 at 20:36
  • $\begingroup$ I would say there kind of is such a thing but it's not very well-defined and (as is often the case) kind of more to do with not understanding what's really going on/seeing something for the first time than anything deeper. $\endgroup$
    – Thompson
    Commented Aug 25, 2016 at 20:37
  • $\begingroup$ Zagier's one sentence proof of Fermat's theorem on the sums of two squares feels like dark magic to me. (But no guarantees on whether other people find it to be dark magic or just obtuse) $\endgroup$ Commented Aug 25, 2016 at 20:41
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    $\begingroup$ I voted to close this is opinion based, I might also have chose too broad or unclear (which were reasons selected by others). The point is that it is not precise what is intended there. For example I do not think that @JMoravitz examples are examples of what is meant there, but maybe they are. Who knows for certain. I also do not think it is generally about proofs by contradiction, or surprising "magic" proofs. $\endgroup$
    – quid
    Commented Aug 25, 2016 at 21:38

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explainxkcd has some great explanations for those questions. Just add "explain" in the url:

http://xkcd.com/1724/ becomes http://explainxkcd.com/1724/

For example, in 1931 Kurt Gödel was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but can be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the set theory, where many statements become impossible to prove and disprove if the axiom of choice is not taken as a part of the axiomatic system.

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    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$
    – Mårten W
    Commented Aug 25, 2016 at 22:30
  • $\begingroup$ You are right, even if this answer was more a tip where to find expanations of xkcd comics. $\endgroup$
    – Kaligule
    Commented Aug 25, 2016 at 22:53
  • $\begingroup$ Added a citation, so everyone is happy :) $\endgroup$
    – Kaligule
    Commented Aug 25, 2016 at 22:55

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