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I am just a man who has an insatiable desire for knowledge.

"For the rest, brethren, whatever is true, whatever is worthy of reverence and is honorable and seemly, whatever is just, whatever is pure, whatever is lovely and lovable, whatever is kind and winsome and gracious, if there is any virtue and excellence, if there is anything worthy of praise, think on and weigh and take account of these things [fix your minds on them]."~ Philippians 4:8


Nov
18
asked Average Amount Of Math or Math-oriented Courses Taken Each Semester
Nov
18
asked Discrete Math Course
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.
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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
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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