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Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically?

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    In fact, this [occasionally useful proposition](http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations) was proved by Russell and Whitehead.2011-12-29
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    You should go read up on set theory, particularly the Peano Axioms. This is a consequence of how the natural numbers and addition on them is defined.2011-12-29
  • 0
    Google "Russel and Whitehead's proof that 1+1=2"! Good Luck.2011-12-29
  • 15
    In many formal developments, "$1+1=2$" is very close to being the _definition_ of $2$ -- so don't expect any very exciting proof.2011-12-29
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    I tried to retag, since [proof-theory] was *completely* wrong. I hope the tag is less wrong now, but if someone thinks it's still not fully fitting - please retag.2011-12-29
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    I don't mind adding more to my answer, if you have any follow up questions or so, feel free to leave a comment below my answer and I will add more information.2012-01-01
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    @HenningMakholm What would be *a* definition of $2$ if not $1+1$? Modulo different symbols (i.e, $SS0$ instead of $1+1$).2016-05-18
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    @HenningMakholm, Re "*many*": Examples?2017-05-15
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    @Pacerier: Everything that builds on Peano Arithmetic, for example.2017-05-15

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