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Tell me the meanings of the following : 1. 2.upper and lower bound of a set

 

Tell me the meanings of the following :


1.


 


2.upper and lower bound of a set


Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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.

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Regards,
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Badiuddin

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