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24232456
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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
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.
May
25
comment How do you respond to “I was always bad at math”?
Join the club! :-) Since it’s usually just small talk, I usually try gently to change the subject. Occasionally I adopt your other approach; I don’t think that it’s led to any ugliness.
May
25
comment Infinite series and its upper and lower limit.
@Hendrik: Ah. It’s not can’t make use of that’s causing the problem, I think, but rather the fact: the fact to which I was referring is the fact that the series is absolutely convergent, which you can’t use to prove that it converges, not the fact that it’s positive.
May
25
comment Infinite series and its upper and lower limit.
@Hendrik: Yes, we’re done — once that proof has been given. But it can’t be given until one has proved the (admittedly easy) result that it uses, and it does have to be given at some point in one’s mathematical education. My point is simply that no matter how you approach the matter, there really is something to be proved.
May
25
answered A property of uniform spaces
May
25
comment Infinite series and its upper and lower limit.
@Hendrik: No, it does not. It merely shows that if the series is convergent — which has yet to be established — then it is absolutely convergent.
May
25
comment Characterization of proper maps using filters
@echoone: You’re welcome.
May
25
answered Equivalent graph related terminologies
May
25
comment Non-self-mapping automorphism implies abelian
@Paul: You’re welcome!
May
25
comment Non-self-mapping automorphism implies abelian
@Paul: Sorry: my mind went walkabout. What I had was silly, but it should be okay now.