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Nov
18
comment Answering Questions For A Poset.
I am so sorry: I copied and pasted the wrong question from my text-book.
Nov
18
revised Answering Questions For A Poset.
deleted 14 characters in body
Nov
18
comment Answering Questions For A Poset.
To answer your question, "Can you figure out what these definitions tell you in terms of your given relation?": If $a$ and $b$ are in the poset, and $a|b$, then $a$ precedes $b$; but if $a$ is a multiple of $b$, then b precedes a. "Note what this entails in terms of comparability." x can only be a maximal with respect to the elements it is comparable to? Similarly, x can only be a minimal with respect to the elements it is comparable to?
Nov
18
comment Answering Questions For A Poset.
@DonAntonio What do you mean? It didn't ask me to write the order.
Nov
18
comment Answering Questions For A Poset.
@DonAntonio The order on the relation is divisibility $|$.
Nov
18
asked Answering Questions For A Poset.
Nov
18
accepted Constructing A Hasse Diagram Using The Covering Relation
Nov
17
comment Reflexive Transitive Closure
Is it possible for you to provide me with a definition that hints at these things? The definition my book provides doesn't even remotely suggest that a covering relation can't be reflexive--actually, my book does not really have nice succinct definition on this concept.
Nov
17
comment Reflexive Transitive Closure
@BrianScott Why isn't a covering relation generally transitive; why isn't it ever reflexive?
Nov
17
comment Reflexive Transitive Closure
What do you mean by this, "If $R$ is already reflexive and transitive, then $R$ is its own reflexive transitive closure, but that’s not the case with your covering relations." A covering relation isn't transitive or reflexive?
Nov
17
accepted Establishing A Covering Relation
Nov
16
asked Reflexive Transitive Closure
Nov
16
comment Establishing A Covering Relation
No, I mean, why can't it be that $(\{a,b\},\{a,b,c\}$ is not in the covering relation, and $(\{a\},\{a,b,c\}$ is?
Nov
16
comment Establishing A Covering Relation
Also, the answer key says that $(\{a\},\{a,b,c\}$ won't be in there, but $(\{a,b\},\{a,b,c\}$. Why couldn't it be the other way around?
Nov
16
revised Establishing A Covering Relation
added 714 characters in body
Nov
16
comment Establishing A Covering Relation
@ThomasAndrews My question is, why does it have to be a proper subset? I edited my post to include the description my book gives on Covering relations.
Nov
16
asked Establishing A Covering Relation
Nov
16
asked Constructing A Hasse Diagram Using The Covering Relation
Nov
16
accepted Definition Of Lexicographic Ordering
Nov
16
asked Equivalence Notation