# Homework Help: Increasing/decreasing intervals for floor function.

1. Nov 25, 2012

### peripatein

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. Nov 25, 2012

### haruspex

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.

3. Nov 26, 2012

### peripatein

Were I to state its decrease/increase intervals, would it be correct then to say there are none?

4. Nov 26, 2012

### peripatein

I mean, would it be correct to say that the floor function has no increase/decrease intervals?

5. Nov 26, 2012

### haruspex

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?