1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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! :-)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook