Question

What is the infimum of the set S = {x:x2 < 16, XEI)​

Answer 1

Given   S = { x :  2 < x  < 16  , x ∈ I )

or S = { x :   x²  < 16  , x ∈ I )

To Find : infimum of the set S

Solution:

infimum  is less than or equal to all elements of  S

if a set has a smallest element, then the smallest element is the infimum for the set.

Here  2 <  x  < 16

Here smallest element is not  available  but its greater than 2

Hence infimum of the set S is 2

supremum is greater than or equal to all elements of  S

Here x  < 16

Hence supremum of set is 16

if question is   x² < 16

=>     - 4 < x  <  4

Then  infimum of the set S is  -4  and supremum of set is 4

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Answer 2

Given   S = { x :  2 < x  < 16  , x ∈ I )  

or S = { x :   x²  < 16  , x ∈ I )  

To Find : infimum of the set S

 

Solution:  

infimum  is less than or equal to all elements of  S  

if a set has a smallest element, then the smallest element is the infimum for the set.  

Here  2 <  x  < 16  

Here smallest element is not  available  but its greater than 2  

Hence infimum of the set S is 2  

supremum is greater than or equal to all elements of  S  

Here x  < 16  

Hence supremum of set is 16  

if question is   x² < 16  

=>     - 4 < x  <  4  

Then  infimum of the set S is  -4  and supremum of set is 4

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