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11440
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location Iowa City, IA, USA
age 56
visits member for 3 years, 5 months
seen 2 days 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".


2d
comment Understanding infinity
Take a look at Ruder Rucker's Infinity and the Mind.
Dec
16
comment “Novel” proofs of “old” calculus theorems
I'll keep my eye open for such results and come back here to include any that I find in the future. However, off-hand (i.e. without possibly extensive searching through my stuff at home) I don't know of anything else.
Dec
15
comment Was there anybody before Cantor who conjectured existence of infinities of different sizes?
A few days after this question was asked (but apparently long enough for me to have fogotten about it), I posted several references that would be useful to this question. See Did Galileo's writings on infinity influence Cantor? at the History of Science and Math stackexchange group.
Dec
12
comment Applications of Singular Functions
You might find something by looking through the reference list I posted in math StackExchange as Bibliography for Singular Functions.
Dec
12
revised “Novel” proofs of “old” calculus theorems
A much better reference included
Dec
11
comment A set with positive measure has a point for which every open interval around it has positive measure
Fortunately I covered myself by saying "at least if $\mu$ isn't pathological enough"!
Dec
11
comment “Novel” proofs of “old” calculus theorems
I don't have access to Bruckner's paper where I'm at, but googling its title along with my name brought up a couple of stackexchange answers of mine that mention results in the paper. One is Importance of a result in measure theory and the other is Construction of a Borel set with positive but not full measure in each interval.
Dec
11
answered “Novel” proofs of “old” calculus theorems
Dec
9
comment A set with positive measure has a point for which every open interval around it has positive measure
I don't see why $B$ has to be a Borel set. The result still holds if $B$ is $\mu$-measurable, and in fact it still holds for an arbitrary subset of the reals if "$B$ has positive $\mu$-measure" is replaced with "$B$ has positive outer $\mu$-measure", at least if $\mu$ isn't pathological enough (and maybe even then -- I'm not sure what the original poster's usage of "measure" might allow).
Dec
9
comment A set with positive measure has a point for which every open interval around it has positive measure
@Passing By: This is weaker than the Lebesgue density theorem. The Lebesgue density theorem says that $\mu$-almost every $x \in B$ is a point at which $B$ has Lebesgue density $1.$ The analogous result behind this question says that $\mu$-almost every $x \in B$ has the property that $B$ has a positive measure intersection with every open interval containing $x,$ a property that is strictly weaker than even the property of having a positive (symmetric) Lebesgue density at $x.$
Dec
8
awarded  Caucus
Dec
8
comment References on filter quantifiers
For limits, see also: Agnew/Morse, Extensions of linear functionals, with applications to limits, integrals, measures, and densities, Annals of Mathematics (2) 39 #1 (January 1938), 20-30; van Douwen, Finitely additive measures on ${\mathbb N},$ Topology and Its Applications 47 (1992), 223-268; Kostyrko/Salat/Wilczynski, $\cal{I}$-convergence, Real Analysis Exchange 26 #2 (2000-2001), 669-685; Penot, Compact nets, filters, and relations, Journal of Mathematical Analysis and Applications 93 #2 (1983), 400-417. [See especially 3. Applications, which begins on p. 406.]
Dec
4
comment Logical contradiction regarding cardinality of sets - help resolve
+1 for I will also say that using $\Bbb C$ for the set of composite numbers is not a good notation.
Dec
3
comment Is $x^{3/2}\sin(\frac{1}{x})$ of bounded variation?
You can do this without integation by making an appropriate comparison with a calculus 2 $p$-series using a variation (pun intended) on the method in my answer to Curve In a Closed Interval with an Infinite Length. Note that you can get an over-estimate for the length by using (limits of) polygonal paths made up of vertical and horizontal segments. (You can get an under-estimate by summing only the vertical segments.)
Dec
1
comment References on filter quantifiers
Possibly relevant is my October 2004 sci.math post "Generalized Quantifiers" (google sci.math archive and Math Forum sci.math archive). FYI, the Math Forum version has a lot of strange formatting errors. See also Real Functions by Brian Thomson, and see Thomson's earlier 2-part survey Derivation bases on the real line (which contain examples and side-detours not in his book).
Nov
25
comment Ordinal exponentiation identity with natural sum of exponents
"simple & natural question" -- Pun not intended?
Nov
25
revised Ordinal exponentiation identity with natural sum of exponents
Added an additional journal article reference
Nov
25
answered Ordinal exponentiation identity with natural sum of exponents
Nov
24
revised How do I convince someone that $1+1=2$ may not necessarily be true?
minor typos in original quote I intended to fix a moment ago and forgot to
Nov
24
comment Ordinal exponentiation identity with natural sum of exponents
I'll look in my copy of Sierpinski's book (at home; I'm at work now) this evening or tomorrow morning, and maybe in some other books as well, although if it's not in Sierpinski I doubt I'll find it elsewhere. I'll let you know tomorrow what I find.