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location Cleveland Heights, OH
age 66
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
26
comment Cauchy filters in metric spaces
@MinimusHeximus: I was merely suggesting the basic idea, not implying that one should use every entourage. Obviously in the metric $\epsilon$-balls are derived from a specific base. However, the little reading that I did in response to this question suggests that the choice of base doesn’t actually matter; whether that’s true for the obvious generalization of this definition, or whether the general definition isn’t the obvious generalization, however, I don’t know.
May
26
answered Number of functions
May
26
comment Cauchy filters in metric spaces
@MinimusHeximus: Basically the same way, I believe; substitute sets of the form $U[x]$ for $U\in\mathscr{U}$ and $x\in X$ for $\epsilon$-balls.
May
26
comment What set theory axioms do I need to believe in uncountable ordinals?
It at least partly answers the question: $\mathsf{ZF}$ is sufficient, since it’s sufficient for the Hartogs’ number argument, but $\mathsf{ZF}$ minus the power set axiom is not.
May
26
revised Characterization of proper maps using filters
added 1390 characters in body
May
26
answered Help with this double summation
May
25
answered Telescoping sum of powers
May
25
answered Prove the Recursion Theorem
May
25
comment How was this really handy bijection thought up of?
@vonbrand: Of course you and I know a number of ways to derive the formula for $|S_n|$, but that’s not really the point: if you already know the formula, there’s no need for $\sigma$ in the first place. I’m addressing the situation in which the OP’s approach is the first derivation of the formula. (And if I were going to assume it known by some other technique, I’d assume that it was known via stars-and-bars, that being far more elementary than binomial coefficients with negative upper numbers!)
May
25
comment Closure and limit of a sequence
@Student: You’re welcome! One of the best and most widely-used undergraduate topology texts is James Munkres, Topology; it has far more than you need for beginning real analysis, but I think that you’d find the parts that are immediately relevant fairly accessible.
May
25
answered How was this really handy bijection thought up of?
May
25
comment Closure and limit of a sequence
@Student: You’re right about (1), and you’ve drawn the correct conclusion from (2). For the missing step, recall that $p\in\operatorname{cl}E$ iff every open ball centred at $p$ has non-empty intersection with $E$.
May
25
revised How was this really handy bijection thought up of?
Two typos.
May
25
answered Closure and limit of a sequence
May
25
comment How do you respond to “I was always bad at math”?
@Lucas: In fact some of them are bragging: this is a genuine point of pride for them. And in my experience mathematicians are in fact likelier to get this response than academics in many other field.
May
25
comment How do you respond to “I was always bad at math”?
Anything is hard if done at a high enough level, but that doesn’t in my opinion justify the first sentence. By normal everyday standards math is easy for some people and hard for others. And if you’re enjoying what you’re doing, long hours of practice do not automatically equate to difficulty. (‘He ain't heavy Mister — he’s m’ brother!’)
May
25
comment Why continuum hypothesis implies the unique hyperreal system, ${}^{\ast}{\Bbb R}$?
@Asaf: ))))))))) Worse yet, I omitted the full stop and the space before the next sentence!
May
25
revised Why continuum hypothesis implies the unique hyperreal system, ${}^{\ast}{\Bbb R}$?
added 3 characters in body
May
25
answered Why continuum hypothesis implies the unique hyperreal system, ${}^{\ast}{\Bbb R}$?
May
25
comment Infinite series and its upper and lower limit.
@Hendrik: You’re welcome! I’m glad to get that sorted.