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

[peripatein]

Homework Statement

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

Homework Equations

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?

 

[tiny-tim]

hi peripatein!

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.

that's correct, but that is monotonic (i think "monotonous" just means "boring" ) …

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

What about increasing/decreasing intervals? Are there none?

yes

(because there's no interval a,b in the whole of which it is increasing)

 

[peripatein]

Hi tiny-tim,
Thanks a lot! :-)