Is [$x$] monotonically increasing?(where $[x]$ means greatest integer function)
2,020
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.
Related videos on Youtube
Author by
sai saandeep
I am an aerospace engineering student at IIT MADRAS.
Updated on July 23, 2022Comments

sai saandeep over 1 year
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.

Crostul over 7 yearsYes, of course it is.

Ben Grossmann over 7 yearsDepending on your terminology (and terminology/definitions are not always universal), one may say that this function is monotonoically increasing but is not strictly monotonically increasing.
