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Math Help - 1+1=2 ?

  1. #1
    Junior Member Kaloda's Avatar
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    Question 1+1=2 ?

    Show that n+n=2n for every real number n.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Kaloda View Post
    Show that n+n=2n for every real number n.
    I like your post title!

    Under the reals we have the distributive property and also commuatitivity of multiplication, thus n+n=n(1+1)=n*2=2n.
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  3. #3
    Junior Member Kaloda's Avatar
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    No, assume that 1+1 is not equal to 2.
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    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Kaloda View Post
    No, assume that 1+1 is not equal to 2.
    I don't follow. You say we are in reals, where 1+1 does equal 2. So either we're not actually in the reals, or you're suggesting making a proof that is not sound because it's based on a false premise. (In fact, by assuming a false premise one can logically "prove" any statement whatsoever.)
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  5. #5
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    Quote Originally Posted by Kaloda View Post
    No, assume that 1+1 is not equal to 2.
    Principia Mathematica - Wikipedia, the free encyclopedia

    Perhaps you should use their work as a guide.

    (From your subsequent posts, your question almost certainly does not belong in the Pre-Algebra and Algebra subforum). It is impossible to know what level of proof you require. Unless you can make this crystal clear, I don't see the point in posting help with your question.
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  6. #6
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    Quote Originally Posted by Kaloda View Post
    No, assume that 1+1 is not equal to 2.
    Then you cannot prove that n+ n= 2n for all n because it is not true for n= 1. Do you mean "Do not assume that 1+ 1= 2" (which is quite different from "assume that 1+ 1 is not equal to 2").

    In Peano's axioms for the natural numbers we have the "successor function", s(n). Addition is defined by
    a) n+ 1= s(n) and
    b) if m\ne 1 then there exist p such that m= s(p) and then n+ m= s(n+ p).

    While 2 is defined as s(1) so it follows that 1+ 1= s(1)= 2.

    If you don't like that then:
    1) How are you defining "1"?
    2) How are you defining "2"?
    3) How are you defining "+"?
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