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Homework Help: How to prove 1+1=2

  1. Sep 13, 2006 #1
    Hi all,

    My teacher once told me that 1+1=2 is provable, mathematically. True enough it can be done after i google it, but why is there a need to prove it so tediously, i can do it with my fingers. :)

  2. jcsd
  3. Sep 13, 2006 #2
    I am not 100% sure but I am pretty sure that it will have something to do with the definition of the real number system and real numbers etc.
  4. Sep 13, 2006 #3


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    Science Advisor

    Actually, it goes back to the construction of the "counting numbers" themselves.

    Why is there a need to prove it? Well, no need at all for the average person. It is most often done as a simple exercise in the use of Peano's axioms for the counting numbers.
  5. Sep 13, 2006 #4


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    Gold Member

    I'm going to assume that, since you're posting this, you do seriously want an answer.

    Consider: when you do it on your fingers, how do you know it's true? Other than because someone, somewhere has told you "it just is, trust me".
  6. Sep 13, 2006 #5


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    Homework Helper

    The difficult part is defining 1 and 2. Once this is done, the proof is almost trivial. Usually this is done using peano's axioms, but this is just one way.
  7. Sep 13, 2006 #6
    what do you mean whether 1+1 =2 is true? ( how can is not be true?)
  8. Sep 13, 2006 #7
    just to add on, say we define 1 as one unit of something

    the 1 + 1 = two unit of somthing = 2

    Unless you let 3 become two unit of something. then 1+1=3
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