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7h
comment staircase length in Whitney's flat norm and Jenny Harrison's natural norm
For whatever it's worth, I don't know why your question generated a down vote. I don't know anything about this topic, but the question doesn't seem ill-posed to me.
7h
comment Discrete Math: Relations
I think what you intended to describe is to have $n$ elements, one from each of $n$ many sets, having (or not having) an "$n$-fold relation". For example, collinearity is a "$3$-fold relation" for points in a plane. See Ternary relation.
13h
comment Dimension of a single coordinate point in $\mathbb{R}^2$?
@River: See affine space and Definition of an affine subspace and What are differences between affine space and vector space?.
Aug
28
answered Can we find uncountably many disjoint dense measurable uncountable subsets of $[0,1]$?
Aug
26
comment Is this function commonly known or has some name?
I don't know about the function itself, but its integral belongs to a certain class of so-called exponential integrals. See here for details.
Aug
26
comment Lebesgue Premeasure via Transfinite Induction
I should have said the 1927 3rd edition of Volume I of Hobson's. (I didn't notice this until later, too late to correct my original comment.)
Aug
26
comment Lebesgue Premeasure via Transfinite Induction
This sounds like the Lebesgue chain notion that was used roughly during the mid 1910s to the mid 1930s. You can find a lot of references by googling the phrase, but perhaps the best place to begin is the 1925 3rd edition of Volume I of Hobson's The Theory Of Functions Of A Real Variable (doesn't seem to be freely available on the internet) and Hildebrandt's 1926 Bull. AMS paper The Borel theorem and its generalizations (see p. 429). The idea of a half-open interval wasn't used, but I believe the same underlying idea is there.
Aug
24
comment Is there an axiomatic approach to ordinal arithmetic?
It was my understanding (I'm not an expert on this topic) that axiomatic developments of ordinal arithmetic are given in texts on proof theory, at least those that deal with the topic of ordinal analysis such as Proof Theory: The First Step into Impredicativity by Wolfram Pohlers, Proof Theory by Gaisi Takeuti, and Proof Theory by Kurt Schütte.
Aug
21
comment Number of equivalence classes of functions of real variable with the a.e relation.
@Asaf Karagila: I didn't know (then or just before reading your comment) that Arturo was a graduate student then, this not being something (for some reason) I recall ever wondering about. On the other hand, I knew who Herman Rubin was, and he was a very frequent poster on sci.math and many other groups.
Aug
21
comment Number of equivalence classes of functions of real variable with the a.e relation.
@Asaf Karagila: If you go back in time some you can find quite a few well known people in sci.math, such as Curtis T McMullen (1998 Fields medal). Even more is available searching google's sci.math archive (Math Forum didn't start until 1996).
Aug
20
comment Reference request for Heine-Borel theorem
Curiously, about 10 minutes after I saw this question, I got my copy of the latest issue of American Mathematical Monthly in the mail, and the first (and longest) article in it is A pedagogical history of compactness by Manya Raman-Sundstrom [August-September 2015 issue, pp. 619-635].
Aug
20
comment Number of equivalence classes of functions of real variable with the a.e relation.
See this 11 January 2007 sci.math post.
Aug
19
comment High School Geometry Text?
I don't know have any textbooks to recommend, but I was curious whether something interesting would turn up if I poked around what's used in some high school honors geometry courses (unfortunately, in the past 20 or 25 years I think "honors" has come to mean little more than what "college prep" meant 40 years ago), and I found this interesting page of parent comments. Anyway, for starters try googling "honors geometry" along with "high school".
Aug
18
comment Prerequisites for differential topology
Guillemin/Pollack's Differential Topology was a fairly well thought of advanced undergraduate survey of this subject when I was an undergraduate (1970s), and it might be worth looking at.
Aug
17
comment Prove that $x - \frac{x^3}{3!} < \sin x < x$ for all $x>0$
My 22 April 2008 AP-calculus post at Math Forum discusses this and gives a lot of 19th century references (all freely available on the internet, although you'll have to google for them).
Aug
17
comment What is a usual order relation?
The usual order relation is the ordering you would assume someone was talking about if the issue of different possible orders had never come up. So $2$ is less than $5,$ $e^2$ is less than ${\pi}^{2},$ $-3$ is less than $-\frac{1}{2},$ etc.
Aug
13
comment Proof that the factorial is nonelementary
In fact, the gamma function doesn't even satisfy an algebraic differential equation -- see Expanded concept of elementary function?.
Aug
12
comment Elementary topology examples
Related question: Motivation for the importance of topology
Aug
11
comment Any use of advanced Abstract Algebra in Differential Geometry?
The differential geometers I've known seemed to be quite knowledgeable in abstract algebra, and even with what little I know, it seems to me that a fair amount of algebra is needed for Lie groups, fiber bundles, homotopy and homology (and algebraic topology in general) applied to manifolds, etc.
Aug
11
comment A beautiful book on arithmetic doesn't treat you like a little baby
Look for old freely available texts, such as Eaton's A Treatise on Arithmetic (1872) and Thomson's A Treatise on Arithmetic (1880). Also, I recently saw a couple of newer extremely good books in a nearby university library, Bakst's 1944 Arithmetic for Adults and Buckingham's 1947 Elementary Arithmetic, but I don't know whether you can easily get a copy of them.