Dynamic Programming Related Questions

[sampahmel]

Hi all,

(1.) Can someone tell me the difference between a compact valued and single valued correspondence?

(2.) I have been seeing repeating themes of "continuity on a compact set". Does that imply boundedness and thus possible to attain maximum?

(3.) What's the difference between Supremum (I know it is the l.u.b.) and Maximum?

Thank you for taking time out to read and to answer.

 

[disregardthat]

(3.) What's the difference between Supremum (I know it is the l.u.b.) and Maximum?

Thank you for taking time out to read and to answer.

Some sets such as the open interval (0,1) have no maximum, but it has a least upper bound, namely 1. This is not the maximum value since it is not contained in the set.

 

[sampahmel]

Some sets such as the open interval (0,1) have no maximum, but it has a least upper bound, namely 1. This is not the maximum value since it is not contained in the set.

Does that mean the maximum is (1-G) where G is the smallest real >0

 

[disregardthat]

Does that mean the maximum is (1-G) where G is the smallest real >0

No such G exists.