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Single most important object in mathematics?

  1. Jul 15, 2009 #1

    tgt

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    For me it would have to be the set of complex numbers. What's yours?
     
  2. jcsd
  3. Jul 15, 2009 #2

    mathman

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    Mathematics starts with the integers, so I would consider them the most important.
     
  4. Jul 15, 2009 #3

    turbo

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    The concept of zero, hands-down.
     
  5. Jul 15, 2009 #4
    The von Neumann hierarchy.
     
  6. Jul 15, 2009 #5

    tgt

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    Well, the complex numbers include both of them (and also the reals).
     
  7. Jul 15, 2009 #6

    Office_Shredder

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    From the empty set you can construct everything.
     
  8. Jul 15, 2009 #7
    I second the empty set.
     
  9. Jul 16, 2009 #8

    To be accurate math starts (in the standard construction) with the natural numbers and sets. From there you derive integers, then rationals, then reals, then complex, then quaternions, then octernian, etc.
     
  10. Jul 16, 2009 #9
    Oh I'm totally all about Graham's number!
     
  11. Jul 16, 2009 #10
    How many dollars I have.
     
  12. Jul 16, 2009 #11

    dx

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    The ideas of 'set' and 'function'.
     
  13. Jul 16, 2009 #12
    the proof, Euclid I 47
     
  14. Jul 16, 2009 #13
    The field of algebraic numbers.
     
  15. Jul 16, 2009 #14
    So what's the LEAST important object in mathematics?
     
  16. Jul 16, 2009 #15
    *insert offensive generalization about hygiene, women, etc.*.. oh snap!
     
  17. Jul 17, 2009 #16
    1 is by far the most important.
     
  18. Jul 17, 2009 #17

    chiro

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    To me its the idea that representation of any kind is abstracted to a mathematical quantity. This fact alone says a lot about the power of mathematics.
     
  19. Jul 18, 2009 #18
    most important: equals sign?
     
  20. Jul 18, 2009 #19
    I third the empty set.
     
  21. Jul 18, 2009 #20
    Im gonna have to read about the empty set.

    The most important thing in mathematics is the concept of numbers. And from there stems everything else.

    But SPECIFICALLY, my absolute favorite is Euler's formula and his Identity.

    [tex]e^{ix}= \cos (x)+ i \sin (x)[/tex]

    [tex]e^{i\pi}+1 =0[/tex]

    The most beautiful relationship ever.
     
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