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A little more about the pedagogy of what it means to be transcendental
[ This is a followup to In simple English, what does it mean to be transcendental? ]A while back a Math SE user posted a comment on my simple explanation of transcendental and algebraic numbers that...
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I vent my rage at dumbass Math SE comments
[ Content warning: ranting ]An article I've had in progress for a while is an essay about the dogmatic slogan that “infinity is not a number”. As research for that article I got Math Stack Exchange to...
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Bad but interesting mathematical notation idea
Zaz Brown showed up on Math SE yesterday with a proposal to make mathematical notation more uniform. It's been pointed out several times that the expressions$$y^n = x \qquad n = \log_y x \qquad...
View ArticleAt last, an internet commenter I can agree with
Browsing around Math StackExchange today, I encountered this question, ‘Unique’ doesn't have a unique meaning, which pointed out that the phrase “Every boy has a unique shirt” is at least confusing....
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Math SE report 2023-02
I had an unusually interesting batch of Math Stack Exchange posts recently.I think all of my answers to these questions are worth reading in full, and if you like the math posts on my blog, you will...
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I liked this simple calculus exercise
A recent Math SE question asked for help computing the value of $$\int_0^{2000} e^{x/2-\left\lfloor x/2\right\rfloor}\; dx.\tag{$\star$}$$( means rounded down to the nearest integer.)Often when I see...
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Math SE report 2023-04: Simplest-possible examples, pointy regions, and...
Polyhedra has more corners than facetsThis one was a bit puzzling because it asked:Is it true that [a polyhedron] has always more/as many corners than facets? I haven't found a counterexample…(By...
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Show how the student could have solved it
A few days ago I offered these maxims about pedagogy:It's not enough to show the student the answer; you should try to show them how to find the answer.It's not enough to show the student how you can...
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Math SE report 2023-05: Arguments that don't work, why I am a potato, and set...
How to shift a power series to be centered at ?OP observed that while the Taylor series for , centered at zero, is a good approximation near , it is quite inaccurate for computing : bigger than about...
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Math SE report 2023-06: funky-looking Hasse diagrams, and what is a...
Is a fourth-degree equation?This is actually a really good question! (You can tell because it's quick to ask and complicated to answer.) It goes back to a very fundamental problem that beginners in...
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Math SE report 2023-09: Sense and reference, Wason tasks, what is a sequence?
Proving there is only one proof?OP asks:In mathematics, is it possible to prove that there is only one (shortest) proof of a given theorem (say, in ZFC)?This was actually from back in July, when there...
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Math SE report 2023-10: Peano's definition of addition is not a tautology,...
Content warning: grumpy complaining. This was a frustrating month.Need an intuitive example for how "P is necessary for Q" means "Q⇒P"?This kind of thing comes up pretty often. Why are there so many...
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