32,480 reputation
888216
bio website blog.plover.com
location Philadelphia, USA
age
visits member for 2 years, 6 months
seen 3 hours ago

I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.


4h
comment Failure of De Moivre's Theorem
@flybynight I'm truly mystified as to what the OP question actually is, and in such cases OP often finds it helpful to get a clear and straightforward explanation of the situation in general.
8h
comment Existence of a minimal generator for a group?
It seems to me that there is no minimal set of generators for $\langle \Bbb Q, +\rangle$, but I have to leave now and can't finish thinking about it until later.
14h
comment Failure of De Moivre's Theorem
When you said “integer powers” in the first sentence, did you mean “non-integer powers”? And I'm not sure what your counterexample is in the second sentence, since $\pm1$ are both square roots of $1$, so it seems that the theorem is working just fine for that case.
17h
comment Euler's Formula, Square root
I don't understand what your question is. What formula are you trying to come up with? What properties do you want it to have?
1d
comment How many undecidable statements are there in ZFC?
Gödel's incompleteness theorem shows that unless ZFC is inconsistent, there must be infinitely many: it constructs one, say $G$, and then you can consider ZFC $\cup\{ G\} $ and apply the theorem again to construct another, and so on.
1d
comment I'm not understanding this puzzle
It could be pretty much anything. What if the first one is “number of squares plus number of places four squares meet”? What if the first one is “Number of vertices of degree at least 3”? What if the first one is “number of rectangles with area at least 2”? Then the answer to the second one is respectively 13, 12, or 27. This kind of puzzle sucks. It takes a smart person to come up with a good puzzle, and this one wasn't.
1d
comment A subset that is closed under multiplication but not addition?
When you are talking about an equation like $x_1+x_2+2 = 0$, you mean the set of pairs $(x_1,x_2)$ that makes the equation true. For example, $(1,-3)$ is a pair satisfying the equation, since $1 + (-3) + 2 = 0$. But $(2, -6)$ is a scalar multiple of that pair and does not satisfy the equation, since $2 + (-6) + 2 \ne 0$. So the set you suggested is not closed under scalar multiplication as you claimed.
1d
comment How does $A_n$ look in Aut$(X)$?
I see now, thanks.
1d
comment How does $A_n$ look in Aut$(X)$?
What does $x-y$ mean when $x,y\in X $?
2d
comment How does $A_n$ look in Aut$(X)$?
In the second paragraph you seem to be saying that $X$ can be any finite set. How do you calculate the rational function $\prod_{\{x,y\}} \frac{\sigma(x)-\sigma(y)}{x-y}$ when $X$ is an arbitrary finite set?
2d
revised Creating intuition about Laplace & Fourier transforms
added 13 characters in body
2d
comment Challenge on Property of Complement in Language
What does $\overline{d(M_1)}$ mean? Is that supposed to be an automaton that accepts the complement of the language accepted by $d(M_1)$?
2d
comment Challenge on Property of Complement in Language
I don't understand your notation here. If $M_1$ and $M_2$ are automata, what does $d(M_1)$ represent? And what do you mean by "union of $M_1$ and $M_2$"? I know how to take unions of languages, but the union of automata is not clear.
2d
revised Is it possible to accurately calculate an irregularly shaped frustum's volume?
edited tags
2d
comment how many infinities are there?
This is essentially asking how many ordinal numbers there are. But there can't be a number of ordinal numbers, or that number would itself be an ordinal number, larger than any other ordinal number, which is absurd. This is the Burali-Forti paradox.
2d
revised Algorithm for finding contradictions in a directed graph that represents implications
added 27 characters in body
2d
revised Steps to solve this system of equations: $\sqrt{x}+y=7$, $\sqrt{y}+x=11$
deleted 2 characters in body
2d
revised Prove that $x\in\mathbb Q$
edited body
Aug
18
revised Anti-symmetric relations
added 1 character in body
Aug
18
revised Anti-symmetric relations
added 1 character in body