Tell me the meanings of the following :1.2.upper and lower bound of a set

Dear araku

An upper bound of a subset S of some partially ordered set ( P, ≤) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is lesser than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound. Properties A subset S of a partially ordered set P may fail to have any bounds or may have many different upper and lower bounds. By transitivity, any element greater than or equal to an upper bound of S is again an upper bound of S, and any element lesser than or equal to any lower bound of S is again a lower bound of S. This leads to the consideration of least upper bound s: (or suprema) and greatest lower bound s (or infima). The bounds of a subset S of a partially ordered set P may or may..

lets analyse above difinition with example.

suppose we have a set  { 5, 10, 34, 13934 }   then  2 and 5 are both lower bounds for the set . but 8 is not

lets another set {24} ,42 is both upper and lower bound for the set and all other numbers are either an upper bound or a lower bound for that set.

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed  solution very  quickly.

 We are all IITians and here to help you in your IIT JEE preparation.

All the best.
 
Regards,
Askiitians Experts
Badiuddin