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X O(y) z

  1. Oct 2, 2004 #1

    Alkatran

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    We all know 2+2=4,2*2=4,2^2=4, etc. So, if we say O(1) means +, O(2) means *, etc. Then we know that 2 O(x) 2 = 4.

    So, how do we solve for x? If we have 3 O(x) 5 = 24, what is x?

    Let's say that - is O(-1), / is O(-2), etc (can you define something that uses what it describes to define itself? (the -)?)

    That would mean
    x O(y) z = t is the same as x = t O(-y) z
    right? What other rules are there that are independent of the level of operation?
     
    Last edited: Oct 2, 2004
  2. jcsd
  3. Oct 3, 2004 #2
    if i define aXb as a^2-b+(a-b)
    and O(3) = X
    then 3 O(3) 5 = 24

    in that case * and / are not the ones u are looking for ... u are preferrably looking for something like + or - ??

    Hmm what exactly is level of operation in this example?

    -- AI
     
  4. Oct 3, 2004 #3

    Alkatran

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    + is O(1)
    - is O(-1)
    * is O(2)
    / is O(-2)
    ^ is O(3)
    sqr() is O(-3)
    etc

    if x O(y) z = t then t O(-y) z = x

    x O(y) 2 = x O(y - 1) x
    (2*2 = 2+2, 3*2 = 3+3, 5+2 = 5 ??? 5 = 7)

    x O(y) 3 = x O(y -1) x O(y - 1) x
    (2*3 = 2+2+2, 3*3 = 3+3+3, 5+3 = 5 ??? 5 ??? 5 = 8)

    I think in this system ???, or O(0), would be some form of increment?
     
  5. Oct 3, 2004 #4
    5*2 = 5+5
    (am i missing something?)

    similarly, 5*3 = 5+5+5

    Also Note that,
    if x O(y) z = t then t O(-y) z = x
    will fail for y=2
    if i place z as 0 ...

    It seems u are trying to develop some sort of system where one can represent one operation in terms of another or something like that ... am i right??

    why don't u take the group theoretic approach?
    tho i am unsure if something like this has been tried before .....

    -- AI
     
  6. Oct 3, 2004 #5

    Alkatran

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    Of course it will fail. You divided by 0! :rolleyes: Just the same as you can't find the 0th root of a number. (what multiplied 0 times will equal...)

    You could say
    x O(y) z = undefined if y < -1 and z = 0
     
  7. Oct 4, 2004 #6
    umm we are not really generalising here are we?
    so what are we looking for?

    -- AI
     
  8. Oct 4, 2004 #7

    Alkatran

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    When you display it like this, it brings up the question what happens because of O() when you pass real numbers, imaginary numbers, 0, etc...
     
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