Is [$x$] monotonically increasing?(where $[x]$ means greatest integer function) Is [$x$] monotonically increasing? (where $[x]$ means greatest integer function). In my book it is given as non monotonically increasing ...--prophetes.ai

Is [$x$] monotonically increasing?(where $[x]$ means greatest integer function) Is [$x$] monotonically increasing? (where $[x]$ means greatest integer function). In my book it is given as non monotonically increasing function. But I think it is monotonically increasing function. Please clarify me. ![enter image description here](

Yes it is.

Informally: The floor function never decreases (it is either constant or increases strictly).

Formally: $[x] \leq [x]+1 = [x+1]$ so by definition the floor function is increasing.