Two differences between supremum and Infimum

Let A be a set in Ɍ (set of all real numbers) . 
A number b said to be supremum if 
1)  b  is upper bund for set A  but to be infimum  b is lower bound for set A.
2)Every number less than b is not an upper bound for set A.    On the other hand, every number greater than b is not lower bound for A. 
Example,
A = {1, 2, 3, 4}
Here, Supremum of set A  is 4 and infimum of set A is 1.

Note that supremum also known as least upper bound and infimum also known as gratest lower bound.

Filed Under: Mathematics on Saturday, July 18, 2015