zero

Discussion in 'Math' started by sanjayladwa, Oct 27, 2006.

  1. sanjayladwa

    Thread Starter New Member

    Oct 26, 2006
    5
    0
    we know that when any number is raised by zero we get 1.can you prove practically and theoritically
     
  2. Papabravo

    Expert

    Feb 24, 2006
    9,898
    1,722
    I think that an exponent of zero being equal to 1 is an empirical choice that allows a function like a^x to be continuous at x = 0.

    If you are familiar with infinite power series then you know that the series for e^x yields the value 1 for x = 0; and because all the terms in x vanish at x = 0, the result is exact.


    This argument is hueristic and lacks rigor but it's the best I can do in my bathrobe.
     
  3. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    143
    There are many possible proofs for this, but one that springs to mind is:

    Take: x^0

    And (strangely): 0 = 0 - 0

    So we can say: x^0 = x^(0 - 0)

    From the laws of indices: a^(m - n) = (a^m)/(a^n)

    We can express: x^(0 - 0) = (x^0)/(x^0)

    Therefore for any value of x, anything divided by itself is equal to 1.

    QED

    Dave
     
  4. sci-3d

    Well-Known Member

    Aug 22, 2006
    51
    0
    Your proof is very clear, Dave.
     
Loading...