# Travis

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bio website location age 32 member for 1 year, 6 months seen yesterday profile views 28

I'm earning my PhD in mathematics and have been employed as an analyst since graduating college in 2003.

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 Sep3 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? Sep2 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. Sep2 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: $\text{rank}(\ \ \ )=0$ Sep2 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.) Sep2 asked Discussion: Differing definitions for the rank of a set Aug26 answered What does $H(\kappa)$ mean? Aug26 reviewed Approve suggested edit on What is the name of $V_\alpha$? Aug26 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. Aug26 asked What is the name of $V_\alpha$? Aug25 comment What does $H(\kappa)$ mean? Ah. I've been stuck in large-cardinal land for the past several days. Good catch. Aug25 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)? Aug25 awarded Commentator Aug25 accepted What does $H(\kappa)$ mean? Aug25 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). Aug25 comment What does $H(\kappa)$ mean? @BrianM.Scott: Much easier to read. :-) I was struggling to see what change you made to the TeX, but then I figured out that somehow with SE's dynamic updating, the page had refreshed but view-source was still giving me the old source until I did a manual refresh. Aug25 comment What does $H(\kappa)$ mean? @BrianM.Scott, I'm new to TeX. Is there a way to add more space between the two rows of your piecewise definition for ${\bigcup}^n(x)$? Aug25 awarded Quorum Aug25 asked What does $H(\kappa)$ mean? Aug25 comment Predicting the next vector given a known sequence @Ang Zhi Ping: I wasn't able to add this comment to his answer, but the Richardson extrapolation that 'example' showed is one of the "more advanced" Numerical Analysis extrapolation methods I mentioned. Aug24 answered Predicting the next vector given a known sequence