Is [$x$] monotonically increasing?(where $[x]$ means greatest integer function)


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

sai saandeep
Author by

sai saandeep

I am an aerospace engineering student at IIT MADRAS.

Updated on July 23, 2022


  • sai saandeep
    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. enter image description here

    • Crostul
      Crostul over 7 years
      Yes, of course it is.
    • Ben Grossmann
      Ben Grossmann over 7 years
      Depending 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.