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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
Nov
15
accepted Maximal and Minimal Elements
Nov
15
accepted Disjoint Equivalence
Nov
15
asked Definition Of Lexicographic Ordering
Nov
15
comment Dual Of A Poset
Shouldn't it be that $x=ny$? Because $x|y$ is equivalent to $y=nx$, then taking the inverse of that would be $x=ny$, which is equivalent to$y|x$
Nov
15
accepted Incomparable Elements In A Poset