The g.l.b . and l.u.b . from analysis that you mention are with respect to the usual partial order (in fact, total order) $leq$. Indeed, we have $2 leq 3 leq 4 leq 6$, so the g.l.b . w.r.t. $leq$ is $2$ and the l.u.b . is $6$. The problem at hand specifies a different partial order,.
This lecture covers the concept of lower bound, upper bound and then least upper bound and greatest lower bound also known as supremum and infimum Access Ful…
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at least one of the these bounds ( l.u.b . and g.l.b .) must be different from the equal values f (a) , f (b) and let this bound be attained at x = c (say) where c is different from a and b i.e.
c e (a, b). Without any loss of generality, we assume that l.u.b . of f is attained at x = c.
• l.u.b and g.l.b … Examples -The set of all natural number denoted by N = {1,2,3…..} or N = {x : x is a positive integer } Real Number : A number which is either a rational or an irrational is called a real number. The set of all real numbers is denoted by R.
The l.u.b . (supremum) of the set of limit points of a sequence is a limit point, as is the g.l.b . (infimum). We hence can refer to lim sup an and lim inf an as the largest and smallest of the limit points of {an } .
