Partial Order on X: Maximal, Minimal, Greatest & Least Elements

  • Thread starter Thread starter PeterWatson
  • Start date Start date
  • Tags Tags
    Partial
AI Thread Summary
The discussion revolves around defining a partial order on the set X = {2,3,4,5,8,9,15,27,45} based on divisibility. Participants are asked to identify the maximal and minimal elements, as well as the existence of a greatest and least element within this set. Additionally, there is a request for a Hasse diagram to visually represent the relationships. The conversation encourages members to share their attempts and specific points of confusion to facilitate better assistance. Engaging with the community can help clarify these concepts effectively.
PeterWatson
Messages
3
Reaction score
0
I'm stumbling on this basic question!

Let X = {2,3,4,5,8,9,15,27,45}.
Define a partial order | on X such that x|y <--> x divides y.

(a) Find the maximal and minimal elements
(b) Is there a greatest element, if so what is it?
(c) Is there a least element, if so what is it?
(d) Draw the Hasse diagram

Please help!
 
Mathematics news on Phys.org
Welcome to PF!

Hi Peter! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

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 »

Similar threads

I Definition of minimal ideal using symbolic logic notation
Replies
3
Views
622
MHB Partial Order Relation on a Functions Set
Replies
3
Views
2K
MHB Partial Order Relation where the Set is not Necessarily Finite
Replies
6
Views
2K
Prove Zorn's Lemma is equivalent to the following statement
Replies
2
Views
2K
Maximal, greatest, minimal and least elements of a set
Replies
1
Views
4K
I Differentiability of a Multivariable function
Replies
1
Views
2K
What is a Partially Ordered Set and its Properties?
Replies
1
Views
2K
I Help with some confusions about variational calculus
Replies
22
Views
1K
Discrete Math: Poset Characteristics and Minimum Element Count
Replies
4
Views
2K
Understanding Least Upper Bound & Greatest Lower Bound in Q+
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top