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F(x)=x-floor function. Is it monotonous?

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Is the function f(x)=x-floor function monotonous? For which intervals does it increase/decrease?

    2. Relevant equations



    3. The attempt at a solution

    Since for every x and y, x-floor function (x) is not necessarily greater/smaller than y-floor function (y), the function cannot be monotonous. For instance, x=3.5 and y=2.8. 0.5 < 0.8. On the other hand, when x=3.9 and y=2.8 0.9 > 0.8.
    What about increasing/decreasing intervals? Are there none?
     
  2. jcsd
  3. Nov 24, 2012 #2

    tiny-tim

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    hi peripatein! :smile:
    that's correct, but that is monotonic (i think "monotonous" just means "boring" :wink:) …

    monotonic means order-preserving, ie x ≤ y => f(x) ≤ f(y) (or ≥)

    strictly monotonic means x < y => f(x) < f(y) (or >)

    see http://en.wikipedia.org/wiki/Monotonic_function
    yes :smile:

    (because there's no interval a,b in the whole of which it is increasing)
     
  4. Nov 24, 2012 #3
    Hi tiny-tim,
    Thanks a lot! :-)
     
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