Travis

59 reputation

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I'm a grad student in mathematics (very near graduation) and have been employed as an analyst since graduating college in 2003.

	59 reputation	bio	website		visits	member for	9 months
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Oct 22	comment	Combinatorial Identity Starting with $n+r-1$ & maybe picking someone NOT on one team & using alg identity is overly complicated. Simpler: start with $n+r$, $n$ can be umpire, $r$ cannot. RHS: pick ump, then from $n+r-1$ left, pick $2r$ & divide them into 2 teams of $r$. LHS: pick the ump, then pick $r$ from $n+r-1$ left to be on a team. From the $n$ not on team one, pick $r$ to be on team 2. Whoops, our ump might be on team two. Forget him for a bit (divide by $n$). Pick someone from the $n-r$ left. If he can be ump, good. Otherwise swap him with the orig ump. All combos from RHS can be gotten this way.
Sep 26	comment	Discussion: Differing definitions for the rank of a set @AsafKaragila: I guess I don't see what you mean by there are new sets using the second definition. When I construct $V_\omega$, $\omega$ is not yet a set so I wouldn't be asking what its rank is. When I construct $V_{\omega+1}$ I now have the set $\omega$ and it's a subset of $V_\omega$ so it's rank is $\omega$. So I don't ever have a set whose rank has not been defined yet. It looks like a "labeling" difference to me. I don't see a hierarchical or structural difference.
Sep 26	accepted	Discussion: Differing definitions for the rank of a set
Sep 26	accepted	What is the name of $V_\alpha$?
Sep 25	awarded	Editor
Sep 21	awarded	Custodian
Sep 3	comment	Discussion: Differing definitions for the rank of a set @AsafKaragila: lol, that's the opposite of what I was asking. I know and understand that. I was asking how does that relate to def 2? How does def 2 seem to introduce new info at limit points?
Sep 2	comment	Discussion: Differing definitions for the rank of a set @AndréNicolas: Ah the shortcomings of the written language. So much non-verbal communication is lost. Actually under the "Ordinals" and "Usefulness in proofs" sections above, I consider it a strength of the first definition that $\text{rank}(\alpha)=\alpha+1$ and every rank is a successor ordinal. Those conditions are universal. I think a hybrid definition would sacrifice the strengths of both definitions.
Sep 2	comment	Discussion: Differing definitions for the rank of a set @AndréNicolas: Before there is the empty set, there is nothing. The empty set is something - it's that nothingness put into a set. You can think of is as zero is the rank of nothingness: $\text{rank}(\ \ \ )=0$
Sep 2	comment	Discussion: Differing definitions for the rank of a set @AsafKaragila: The part about sets existing once they are elements instead of subsets (hence subclasses) makes sense. Could you expound upon how the second definition implies (or seems to imply) new information is added at limit stages? (Not the philosophy - not why you want limits to be accumulations instead of introducing new material - that I already understand, but how the definition relates to this philosophy.)
Sep 2	asked	Discussion: Differing definitions for the rank of a set
Aug 26	answered	What does $H(\kappa)$ mean?
Aug 26	reviewed	Approve suggested edit on What is the name of $V_\alpha$?
Aug 26	comment	What is the name of $V_\alpha$? Well "the $\alpha$th level ..." is more creative than anything I was able to come up with just now.
Aug 26	asked	What is the name of $V_\alpha$?
Aug 25	comment	What does $H(\kappa)$ mean? Ah. I've been stuck in large-cardinal land for the past several days. Good catch.
Aug 25	comment	What does $H(\kappa)$ mean? @Asaf: Why did you change the (large-cardinals) tag to (cardinals)? Since $\kappa$ is a strongly inaccessible cardinal, which ZFC can't prove exists, doesn't that meet the criteria for (large-cardinals)?
Aug 25	awarded	Commentator
Aug 25	accepted	What does $H(\kappa)$ mean?
Aug 25	comment	What does $H(\kappa)$ mean? @BrianM.Scott: Thanks. It was the revision history that showed me my view-source was out of date (even though I opened view-source after SE dynamically refreshed the page).