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The functions that have atleast 1 pair of m and M such that , where m and M are called bounded functions. The greatest such value of m is known as Greatest Least Bound (glb) and smallest value of such M is known as Least Upper Bound (lub).
Finding glb and lub of f (x)= sin x
First we have to check that it is bounded or not. We know that . Thus Sin x is a bounded function. There can be infinite m and M. Minimum value of sinx is -1 and maximum value is 1. Thus glb=-1 and lub=1.