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location Cleveland Heights, OH
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visits member for 3 years, 1 month
seen Jan 2 at 12:05

Professor emeritus at Cleveland State University. I’m a set-theoretic and general topologist with an interest in combinatorics. I’m also interested in linguistics, especially historical linguistics.


May
27
comment Create non-substantive filter, belonging chief ultrafilter
@Alexander: Thanks, and thanks for the ping.
May
27
answered Create non-substantive filter, belonging chief ultrafilter
May
27
answered The 'compactness cardinal' of a space
May
27
revised How many epsilon numbers $<\omega_1$ are there?
added 211 characters in body
May
27
answered How many epsilon numbers $<\omega_1$ are there?
May
27
comment Create non-substantive filter, belonging chief ultrafilter
Mariya: Let $E=\{2n:n\in\Bbb N\}$, and let $\mathscr{F}=\{F\subseteq\Bbb N:F\supseteq E\}$; clearly $\mathscr{F}$ is a principal filter on $\Bbb N$. Let $\mathscr\{U\}$ be any non-principal ultrafilter on $E$, and let $\mathscr{G}=\{U\cup A:U\in\mathscr{U}\text{ and }A\subseteq\Bbb N\setminus E\}$: $\mathscr{F}\subseteq\mathscr{G}$, and $\mathscr{G}$ is a non-principal ultrafilter on $\Bbb N$.
May
27
comment Create non-substantive filter, belonging chief ultrafilter
This was closed far too hastily. Chief and substantive are pretty clearly mistranslations of some word whose meaning in this context is principal. The question almost certainly asks us to construct a non-principal filter $\mathscr{F}$ that can be extended to a principal ultrafilter $\mathscr{G}$.
May
27
comment Rudin Principles Theorem 2.40: Every k-cell is compact.
@Bryan: I’m not sure exactly which statement you’re trying to prove.
May
27
comment Enumerate partitions of identical objects
@joriki: Thanks. (It's nice to know that my programming instincts aren't completely dead!)
May
27
comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
@Alan: Sure: your $r$ is my $n$, and your $n$ is my $k$.
May
27
comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
@Alan: No, the sum is over $n$; $k$ is fixed throughout.
May
27
comment A question on countability of isolated points of a subset of R
@user68099: Glad you found it useful. It extends essentially unchanged to separable metric spaces, since they are precisely the second countable metric spaces.
May
27
answered How to use induction to prove this argument?
May
27
reviewed Approve suggested edit on How to obtain conditional cumulative probability
May
27
answered prove $\inf S = -\sup (-S)$
May
27
comment What are some examples of proof by contrapositive?
This question has a nice example; see especially the discussion in my answer. This question and its answer are another, and this, this, and this should also be of interest. These are just a few that I could easily find.
May
27
awarded  Nice Answer
May
27
comment Differentiate $g(t)= {e^t - e^{-t} \over e^t + e^{-t}}$
@Mariana: I did wonder if that was the case, but sometimes books or teachers do ask questions like that. No harm done!
May
27
revised Differentiate $g(t)= {e^t - e^{-t} \over e^t + e^{-t}}$
added 547 characters in body
May
27
answered Differentiate $g(t)= {e^t - e^{-t} \over e^t + e^{-t}}$