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.
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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.