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Increasing/decreasing intervals for floor function.

  1. Nov 25, 2012 #1
    Hello,

    1. The problem statement, all variables and given/known data

    In which intervals is the floor function decreasing/increasing?

    2. Relevant equations

    3. The attempt at a solution

    I first presumed it was increasing for every integer x, now I am not sure. May anyone please confirm/debunk? Is it also monotonic for every integer x?
     
  2. jcsd
  3. Nov 25, 2012 #2

    haruspex

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    An integer is not an interval. This is a question about intervals of reals rather than integers.
    Need to clarify whether you mean strictly increasing or merely non-decreasing.
     
  4. Nov 26, 2012 #3
    Were I to state its decrease/increase intervals, would it be correct then to say there are none?
     
  5. Nov 26, 2012 #4
    I mean, would it be correct to say that the floor function has no increase/decrease intervals?
     
  6. Nov 26, 2012 #5

    haruspex

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    It certainly has no strictly decreasing intervals. Beyond that, I can't answer without knowing exactly what is meant by a function f having an increasing interval [a,b]. It could mean:
    - f(y) >= f(x) whenever a <= x < y <= b (i.e. non-decreasing)
    - f(y) > f(x) whenever a <= x < y <= b (strictly increasing)
    - (f(y) >= f(x) whenever a <= x < y= < b) & (f(a) < f(b)) (strictly increasing over the interval as a whole, and non-decreasing within it)
    Do you have a definition?
     
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