Question #4929

Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the given set.
[5,7]

Expert's answer

S=[5,7].

The set of upper bound elements is the set of numbers which

are greater than or equal to every element of S.

So, it is [7, +inf) and the

least element is 7.

The set of lower bound elements is the set of numbers

which are less than or equal to every element of S.

So, it is (-inf, 5] and

the greatest element is 5.

So, Sup(S) = 7 and Inf(S) = 5.

The set of upper bound elements is the set of numbers which

are greater than or equal to every element of S.

So, it is [7, +inf) and the

least element is 7.

The set of lower bound elements is the set of numbers

which are less than or equal to every element of S.

So, it is (-inf, 5] and

the greatest element is 5.

So, Sup(S) = 7 and Inf(S) = 5.

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