Increasing/decreasing intervals for floor function.

[peripatein]

Hello,

Homework Statement

In which intervals is the floor function decreasing/increasing?

Homework Equations

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?

 

[haruspex]

I first presumed it was increasing for every integer x

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.

 

[peripatein]

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

 

[peripatein]

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

 

[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?