Dynamic Programming Related Questions

AI Thread Summary
The discussion addresses key concepts in dynamic programming, focusing on the distinctions between compact valued and single valued correspondences. It explores the implications of continuity on compact sets, particularly regarding boundedness and the attainment of maximum values. The difference between supremum and maximum is clarified, noting that some sets, like the open interval (0,1), have a least upper bound but no maximum. The conversation emphasizes that the maximum cannot be defined as (1-G) where G is the smallest real number greater than zero, as no such G exists. Overall, the thread provides insights into fundamental mathematical principles relevant to dynamic programming.
sampahmel
Messages
20
Reaction score
0
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.
 
Mathematics news on Phys.org
sampahmel said:
(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.
 
Jarle said:
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
 
sampahmel said:
Does that mean the maximum is (1-G) where G is the smallest real >0

No such G exists.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Line count in a simple program
Replies
16
Views
3K
MHB Dynamic programming: which recurrence relation do we use?
Replies
2
Views
1K
Saving the state of a program versus running the program
Replies
22
Views
2K
A Show positivity and boundedness of a non-linear system
Replies
2
Views
499
Programs Choice of Master's degree program, Physics vs. Applied Math
Replies
2
Views
2K
A MOND Theory Primer: Stacy McGaugh's Research Program Explored
Replies
11
Views
4K
I Time Before Big Bang: Relational Dynamics & Singularities
Replies
2
Views
2K
Modeling Air Compression Cylinder
Replies
45
Views
5K
MHB Finding exact 3d coordinates in a falling pipe system with corners
Replies
20
Views
4K
I Can chatgpt accurately calculate expected lengths in Pascal's triangle?
2
Replies
66
Views
6K

Hot Threads

Recent Insights

Back
Top