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Why 1+1 =2 on the 20 greatest equation list?

  1. Feb 17, 2008 #1
    I'm doing assignment which concern the 20 greatest equation, but i can't figure out why 1+1=2 is in it?
  2. jcsd
  3. Feb 17, 2008 #2
    Maybe it's like Time's Person of the Year where they select based on influence rather than being good or bad, so they choose people like Stalin and Hitler. Maybe 1+1=2 is the Adolf Hitler of equations.
  4. Feb 17, 2008 #3
    Its the first equation that everyone learns.

    Hence, why it's so great.
  5. Feb 17, 2008 #4


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    Greatest equations??

    Why do you think 1+1=2 is an equation?
  6. Feb 17, 2008 #5
    Cause it proves addition works ?
  7. Feb 17, 2008 #6
    Because it demonstrates equivalence which is really the most basic function of an equation isnt it?

  8. Feb 17, 2008 #7
    That is definitely an equation.
  9. Feb 17, 2008 #8
    because it's not as simple an equation as everybody thinks it is. It actually takes a lot of effort to prove it.
  10. Feb 17, 2008 #9
    If you have to prove to yourself that 1 + 1 = 2, then maybe you should find a different field to work in.
  11. Feb 17, 2008 #10
    Maybe you should try it..
  12. Feb 17, 2008 #11


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    Well, the proof can be found in Russell/Whiteheads Principia Mathematica (Yes, that really is the name of the books) and it is far from trivial.
    1+1=2 is a very fundamental equation in all work on the foundations of mathematics.
  13. Feb 17, 2008 #12
    If I have one carrot:


    And then add another carrot:


    I now have TWO carrots:


    Also, for those actually debating whether 1 + 1 = 2 is an equation: wtf is wrong with you? There is an EQUALS sign right there. That is what defines an equation, no?
  14. Feb 17, 2008 #13


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    The problem is that this is only an argument (albeit a very plausible one), not a proof. It would be "good enough" in most sciences but not in mathematics.
  15. Feb 17, 2008 #14
    Adding a carrot with another to obtain two carrots just happens to be a convenient application of set theory :biggrin: - it doesn't prove nor show anything.

    Here is a simple argument. We define 1 + 1 as the number of objects in a set that is 1-1 with {1}U{1}. Fortunately, {1,2} is 1-1 with {1}U{1}. Now {1,2} is represented by a cardinal number, that is 2. Is there another set of the form {1, 2, ... n} that satisfies the aforementioned conditions? If there was, the set representing it would also be 1-1 with {1,2}. However, no such subset of N exists. Therefore, 2 is the unique answer to 1 + 1.
    Last edited: Feb 17, 2008
  16. Feb 17, 2008 #15
    That's a lot of jargon there. I wish I understood it. :(
  17. Feb 17, 2008 #16


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    That's a 'tude much more open to learning something new than 'wtf is wrong with you'. :rolleyes:
  18. Feb 17, 2008 #17
    It all depends on context. For instance, the approach would be different using:
    then it would be using category theory.
  19. Feb 17, 2008 #18
    Who the hell is making a list of the "20 greatest equations"?
  20. Feb 17, 2008 #19
    I don't know, but if the Pythagorean theorem isn't on it then it's a sucky list.

    1 + 1 = 2 (or for that matter a + 1 for any integer a) should be fundamental to the definition of integers. You can't construct an ordered field of integers without defining their order, which means that for any integer you should be able to trivially say what the next one is. Sometimes mathematicians try to do very simple things with complicated tools, and it's rather like using a Rube Goldberg machine instead of a screwdriver. I tend to favor more concise solutions...
  21. Feb 17, 2008 #20
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