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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.


Jul
18
comment Different meanings of math terms in different countries
HCF is definitely unusual in the U.S. On the other hand, it’s completely normal (to me, at least) to speak of cancelling common factors, pulling out a common factor, being off by a factor of $2$, etc. I don’t know whether it’s just me or something more widespread, but I think that I tend to use divisor when the notion of division is more prominent and factor when the notion of multiplication is more prominent. (That is, of course, more than a bit fuzzy!)
Jul
18
comment Different meanings of math terms in different countries
Things may have changed, but I learnt both divisor and factor in school (in the U.S.).
Jul
18
answered Formulas for mappings between power set $P_n$ and $1, \ldots, 2^n$
Jul
17
answered Baby Rudin 2.26 Infinite subsets with limit points implies compactness
Jul
17
answered reflexive and antisymetric relation
Jul
17
answered How to show if $A \subseteq B$, then $A \cap B = A$?
Jul
17
comment The perception of mathematics
I’m not sure what you mean by having a negative perception of mathematics. If it means having had unpleasant experiences with mathematics, not understanding it, etc., then at least a quarter of the statement is probably true: there is a widespread negative perception of mathematics outside academia. If it means believing that mathematics is useless, not worth studying, etc., then I’m not at all sure that it’s true. And I’m not at all sure that there is a widespread negative perception of mathematicians. Widespread lack of understanding, yes; negative perception, not at all clear.
Jul
17
comment Proving an Identity involving $4^N$
You’ll find both combinatorial and non-combinatorial proofs here and here.
Jul
17
comment Intuition of Empty Set in Ordered Pair
@LePressentiment: You’re very welcome.
Jul
16
awarded  Good Answer
Jul
16
revised Markov Chain with two states
deleted 144 characters in body
Jul
16
answered Markov Chain with two states
Jul
16
answered In which of the following cases is there no continuous function $f$ from the set $S$ onto the set $T$?
Jul
16
comment In which of the following cases is there no continuous function $f$ from the set $S$ onto the set $T$?
People generally interpret all capitals as SHOUTING; it’s not a good idea.
Jul
16
revised In which of the following cases is there no continuous function $f$ from the set $S$ onto the set $T$?
LaTeX, formatting, got rid of shouting.
Jul
16
answered Subspace over a line in a plane
Jul
16
comment Subspace over a line in a plane
Ah, okay. I’ll give you some hints for both problems, but the first one really does get a bit difficult.
Jul
16
comment Subspace over a line in a plane
In both problems it depends on the specific line. The second problem is much easier than the first: there are only two cases. The first has several cases, and two of the resulting topologies are unfamiliar. Are you sure that the problem does not say anything about which line(s) you’re to consider?
Jul
16
comment Subspace over a line in a plane
I don’t know what you mean by $\Bbb R_d$, because we don’t normally talk about a dictionary order on a space that is not a product. I suspect that you mean $(\Bbb R\times\Bbb R)_d$, the dictionary order topology on $\Bbb R\times\Bbb R$, but that’s not what you wrote.
Jul
16
comment Subspace over a line in a plane
Do you mean that $L$ is a line in the plane? And in (2) do you mean the dictionary order topology on $\Bbb R\times\Bbb R$? We don’t normally think of $\Bbb R$ itself as having a dictionary order topology. (And if we did, it would be the ordinary Euclidean topology.)