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location Cleveland Heights, OH
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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 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 $g(t)= {e^t - e^{-t} \over e^t + e^{-t}}$
May
27
revised Solving summation $2n+2^2(n-1)+2^3(n-2)+…+2^n$
added 493 characters in body
May
27
answered Solving summation $2n+2^2(n-1)+2^3(n-2)+…+2^n$
May
26
revised Partition Properties
Added link.
May
26
comment Interesting Normality Condition (topology)
@Eric: No, the chimney analogy is very physical: one way to climb a rock chimney (or a house chimney, if it’s big enough) is to brace your feet against one side and your shoulders against the other. Then you step up with your feet (building $G_{n+1}$ from $G_n$) and then use your hands behind you to slide your shoulders up the same amount (building $H_{n+1}$).
May
26
answered Prove if $n^2$ is even, then $n$ is even.
May
26
revised Interesting Normality Condition (topology)
added 372 characters in body
May
26
answered Interesting Normality Condition (topology)
May
26
comment Interesting Normality Condition (topology)
Did you want $A\cap\operatorname{cl}V_i$ to be empty, rather than $A\cap V_i$?