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11439
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location Iowa City, IA, USA
age 55
visits member for 3 years, 3 months
seen 14 hours ago

Primary Mathematical Interests:

Study and use of negligible sets, especially involving porosity notions and fractal dimension notions.

Application and refinements of the Baire category method for proving existence.

Classical point set theory and real function theory.

History of nowhere differentiable continuous functions and history of the topics above.

My email address has the form "first-name period last-name at YAHOO period COM".


21h
answered Other Useful Series Tests
1d
comment What is a Lattice?
What does your friend's textbook or class notes have to say about lattices? If it were me and I didn't know the term, and if I also thought I could still be of assistance, I would ask to look at these. However, I suspect I would probably just say "sorry, I don't know anything about lattices, so I don't think I can be of any help". That said, maybe some of the results from a google search for "lattice" {AND} "discrete mathematics" could help.
Oct
17
comment Will computers one day start creating and proving math for us?
@Georges Elencwajg: FYI, here is a similar comment of mine.
Oct
17
comment Will computers one day start creating and proving math for us?
I think a more relevant question is whether we can make much sense of the mathematics that intelligent AI's 100+ years from now will be doing. I'm thinking it'd be like a child just learning about 2-digit integer multiplication trying to make sense of spectral sequences.
Oct
17
comment Translation request: geometry problem stated in Korean
Maybe these google image search results will help.
Oct
17
comment Name of equation
I don't know about this specific equation, but it belongs to a class of equations called reciprocal equations. Many of the older freely available books on the topic "Theory of Equations" will have a lot of information about such equations.
Oct
17
comment Trigonometry textbook or tutorial
@Ishfaaq: Several freely available digital copies of Loney's trigonometry book can be found here‌​. For mathos, there are other authors of similar (having many advanced topics) freely available texts, such as those by Isaac Todhunter, Ernest William Hobson, Clement Vavasor Durell and Alan Robson (co-authors), Elias Loomis, Émile Gelin, John Casey, Joseph Alfred Serret, etc.
Oct
16
comment A very weird connected subset of $\mathbb R^2$
Google "explosion point" along with "connected".
Oct
15
comment What's the relationship between Borel set and set whose boundary is measure zero?
For a non-constructive answer to the first question, note that there are $2^c$ many subsets of the boundary of the unit disk in the plane, all of which have (planar) measure zero, and only $c$ many of these can be Borel sets, so most subsets of the boundary of the unit disk have the property that its union with the open unit disk is not a Borel set (non-Borel union Borel is non-Borel), and all the boundaries of these non-Borel sets have measure zero.
Oct
14
comment Any closed subset of $\mathbb C$ is the set of limit points of some sequence
For a more interesting result, prove that such a sequence can always be chosen so that for each point in the closed set, there exists a subsequence convering to that point whose indices have upper asymptotic density $1$.
Oct
14
comment Any closed subset of $\mathbb C$ is the set of limit points of some sequence
Very similar to Given closed $C \subseteq \mathbb{R}$ find a sequence with subsequences convergent to every point in $C$ and nowhere else.
Oct
14
comment Any closed subset of $\mathbb C$ is the set of limit points of some sequence
@Andres Caicedo: Perhaps $(r_{n})$ is intended to be a sequence of elements in the closed set that is dense in the closed set?
Oct
13
comment Completeness of the space of sets with distance defined by the measure of symmetric difference
By coincidence, I was looking at a paper this weekend that makes use of this metric. See the top half of p. 35 of Harry Max Schaerf, On the continuity of measurable functions in neighborhood spaces, Portugaliae Mathematica 6 #1 (1947), 33-44. The paper is freely available on the internet.
Oct
10
comment Completeness of the space of sets with distance defined by the measure of symmetric difference
FYI, I gave several references and applications to this metric in this 13 May 2005 sci.math post. See especially the paragraph beginning with "Note: This metric space has a number of interesting uses". I think this metric originated from Nikodym in the late 1920s, but I don't have my notes on this topic with me now to look it up. Finally, in that 2005 post I mention how to prove completeness in the paragraph that begins with "ADDITIONAL FACT: M[0,1] is a complete metric space".
Oct
10
comment Book about the foundation of math?
I recently discovered that a digital copy of the 1965 edition of Wilder's Introduction to the Foundations of Mathematics is freely available (and apparently legally available) on the internet.
Oct
9
comment Examples of functions that do not have a limit as x approaches 2
An example of a different nature than those given so far is $f(x) = \sqrt{1-x}.$
Oct
8
revised Solving algebraic fraction problems
converted math expressions to Latex form
Oct
8
comment Book Request: Taylor's Theorem for functions $f: \Bbb R^n \to \Bbb R^m$
Unless you're looking for something rather unusual (e.g. do you really mean $f:{\mathbb R}^n \rightarrow {\mathbb R}^m$ and not $f:{\mathbb R}^n \rightarrow {\mathbb R}),$ it seems to me that most any advanced calculus text would work. C. H. Edwards' Advanced Caclulus of Several Variables has one of the nicest treatments that I know of.
Oct
8
answered Algebraic topology in high school?
Oct
7
comment Baire related problem
Are you sure you mean $n$-fold composition, and not $n$th derivative? This reminds me of a result that Ralph Boas has written a lot about, for what it's worth.