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I Circular Reasoning and Impossible Equation

  1. Oct 27, 2016 #1
    Suppose there is a problem such that in order to know a variable x, you have to know a variable y. But in order to know variable y, you have to know the variable x. Because of this circular dependency, wouldn't it be impossible to write any sensible equation containing x and y?
  2. jcsd
  3. Oct 27, 2016 #2
    You can definitely write an equation but you cannot get some finite set of values for x and y only for which that equation will be true it will be true for a large number of ordered pair (x,y). It will be some thing like identity and not an equation!
  4. Oct 27, 2016 #3
    That makes sense. Thanks.
  5. Oct 27, 2016 #4


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    Staff: Mentor

    What if ##x = 2y## and ##y = x - 1##?
  6. Oct 28, 2016 #5
    They are two independent equations and will give you the solution for a unique ordered pair (x, y).
  7. Oct 28, 2016 #6


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    Take, for example, x=y. From this you can determine neither x nor y. Nevertheless, the equation is very sensible, i.e. contains a lot of useful information. For instance, if x is your position and y is the position of your wallet, and you are a tourist lost in Rio De Janeiro, you will be very happy to know that x=y. :smile:
  8. Oct 28, 2016 #7


    Staff: Mentor

    A unique solution is quite different from a solution set that is infinitely large.
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