32,291 reputation
786211
bio website blog.plover.com
location Philadelphia, USA
age
visits member for 2 years, 5 months
seen 10 hours ago

I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.


21h
comment Complex numbers in polar form
I had to define it specially for your post, using \def.
22h
comment Why is (European) money in units of $1,2,5,10,20,50, \cdots\;$?
I recommend that you read the “preferred number” article in Wikipedia; I think it is most relevant to your question.
2d
comment How do mathematicians know what is known?
If I understand your question correctly, the problem was solved by Gauss. Number of monic irreducible polynomials of degree p over finite fields
2d
comment Fun quiz: where did the infinitely many candies come from?
@did I have not found as many articles as I expected for supertasks. If I don't find at least ten posts for which supertasks is appropriate by this time tomorrow, I will delete the tag. I'll also delete it if almost all the articles I find are tagged with paradoxes.
2d
comment Fun quiz: where did the infinitely many candies come from?
@dstathis I removed it because I thought it was not appropriate. If you want to re-add it, I won't remove it a second time.
2d
comment Fun quiz: where did the infinitely many candies come from?
@did I'm not sure what your question is. For every tag there is a period of time at which there are only 2 questions with that tag. Since this tag is only 5 minutes old it's not surprising that there should be few questions tagged with it.
2d
comment Fun quiz: where did the infinitely many candies come from?
Related: Paradox: increasing sequence that goes to 0?. It also came up here last week, but I can't find the post.
Jul
28
comment how to show that $\mathbb{Q}[\sqrt[3]{2}]$ is a field? (by elementary means)
You make a $\sqrt[3]2$ by writing \sqrt[3]{2}. Reference guide here.
Jul
28
comment Graph partition that span a third of edges
Very nice, thanks.
Jul
28
comment Are there any well known mathematicians who published very little?
@pushpen.paul My suggestion is that Christian Goldbach is not a significant mathematician, and that it is trivial (and not an answer to the question) to find examples of nonmathematicians who have no mathematical publications.
Jul
25
comment How do I turn my verbal argument into something formal in [Real Analysis]? (proving every compact set is bounded)
I'm glad I could help.
Jul
25
comment How do I turn my verbal argument into something formal in [Real Analysis]? (proving every compact set is bounded)
@quantumdot Yes, compact sets are special in exactly this way. The example to think of is the open interval interval $I^\circ=(0,1)$ (not compact) and the closed interval $I=[0,1]$ (compact). $I^\circ$ can be covered by the family $\left(\frac1{n+2}, \frac 1n\right)$ for $n\in\{1,2,3,\ldots\}$, and there is no finite subcover of this family that still covers $I^\circ$. But this family does not cover $I$, and to cover $I$ you have to add at least one more open set to the family, and no matter how you do it, the extra sets plus a finite subfamily of the original family will cover $[0,1]$.
Jul
25
comment A consistent set of formulas
@dstathis It's disjunctive syllogism. if you know that $\psi$ or $\sigma$ is true, and you know that it's not $\psi$, then it must be $\sigma$.
Jul
25
comment In Cantor's Diagonalization Argument, why are you allowed to assume you have a bijection from naturals to rationals but not from naturals to reals?
Here's another relevant discussion: Should a Cantor diagonal argument on a list of all rationals always produce an irrational number?. I think my answer there may be helpful.
Jul
23
comment Find scaling factor that minimizes f(x) - round(f(x))?
By "particular kind of rounding" I mean what do you mean when you say "I round it to $\operatorname{round}(f(x))$". It's your question, and it seems to have something to do with something you call "rounding", but I don't know what you mean by that, and you didn't say.
Jul
23
comment Find scaling factor that minimizes f(x) - round(f(x))?
Do you have some particular kind of rounding in mind? Are there any constraints on the behavior of $\operatorname {round}$?
Jul
23
comment Primitive Recursive Predicate Problem
This is also an exact duplicate of math.stackexchange.com/questions/869545/…
Jul
22
comment An arithmetic sequence whose members do not contain the digit ‘9’
An example with length 72 is $1 + 125n$ for $n\in[0..71]$. The last 3 digits of the elements repeat with period 8, and happen not to contain any nines. The leading digits increase at a rate of 1 per 8 elements, so don't reach 9 until the 72nd element.
Jul
22
comment How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?
This related question asks how one would determine, in 1847, that ${\left(\pi^\pi\right)}^{\left(\pi^\pi\right)}$ is not an integer. Alexander Walker's brilliant answer deserves a look.
Jul
22
comment Is there a proof of (non)existence of a proper universal combinator?
I did not hear back from Bellot.