Question

Give an example of a set which is bounded below but not bounded above.​

Answer 1

One example of a set which is bounded below but not bounded above is

$\sf \{ \: {2}^{n} : n \in \: N \: \}$

Given :

A set which is bounded below but not bounded above

To find :

An example

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that the set is bounded below but not bounded above

Step 2 of 2 :

Find an example

Let us consider the set

$\sf S = \{2, {2}^{2} , {2}^{3} , \: . \: . \: . \: ., {2}^{n} , \: . \: . \: . \: . \}$

$\sf = \{ \: {2}^{n} : n \in \: N \: \}$

Since there exists the element 2 in S such that x ≥ 2 for every x ∈ S

So the set S is bounded below

More over Inf S = 2

But we observe that there exists no element m in S such that x ≤ m for every x ∈ S

So the set S is not bounded above

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