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I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.

You can email me at mjd@plover.com.


16h
comment The drawer has M different colored socks. What is the least amount of socks I that I need to draw to guarntee N pairs
There are general formulas, and it is not too hard to find them. I suggest that instead of considering fifty pairs of socks, you consider two pairs. And instead of considering 50 colors, you consider 3 colors. You may get some ideas that will lead you to the solution of the general problem.
17h
comment give a group that is isomorphic to the figure.
Yes, that is exactly correct.
17h
comment A basic question of basic writing
I don't think it would be wise to use $\equiv$, which almost always means modular equivalence. Simple $=$ is correct, and Grigory Ilizirov gives several other options.
17h
comment A basic question of basic writing
\stackrel can be useful here. For example \stackrel\Delta= is $\stackrel\Delta=$.
18h
comment Definition of the sum of natural numbers
@Trevor Feel free to edit.
21h
comment Give me an idea
Post the question in the original language, and let someone else translate it.
1d
comment Find orbit of $1$ for $\sigma$
@Travis: It's standard to talk about the orbit of some element of a set $X$ under $g$ where $g$ is an element of a group that acts on $X$. I checked Fraleigh A First Course in Abstract Algebra to confirm and found that this question is Exercise 8.10 from that book.
1d
comment Let $G$ be a group and $u \in G$ be a fixed element. By the following, prove that $(G,\bullet)$ is a group.
There is a general theorem that if $\bullet$ is an associative operation on a set $G$ for which $u$ is a left and right identity, and $b'$ is a left inverse for $b$, then $b'$ is also a right inverse for $b$. In general, any three of the four properties (left identity, right identity, left inverse, right inverse) imply the fourth, so that $\langle G, \bullet\rangle$ is a group, and it is a well-known fact that left inverses in groups are the same as right inverses.
1d
comment Prove $\overline{B} - (A-\overline{B}) \subseteq \overline{B}$
It couldn't hurt, but my sense is that OP doesn't need the tutorial as much as he needed to be told to stop putting $ $ between every two symbols.
1d
comment Prove $\overline{B} - (A-\overline{B}) \subseteq \overline{B}$
Even so, there is no reason to write x $\in$ $\overline{B}$ instead of simply $x\in\overline{B}$.
1d
comment Prove $\overline{B} - (A-\overline{B}) \subseteq \overline{B}$
You should not write x $\in$ $\overline{B}$ $\,$^$\,$x$\,$$\in$$\,$($\overline{A}$$\cup$$\overline{B}$), which comes out as «x $\in$ $\overline{B}$ $\,$^$\,$x$\,$$\in$$\,$($\overline{A}$$\cup$$\overline{B}$)». Instead, it looks better and is easier to write simply $x \in \overline{B}\land x\in(\overline{A}\cup \overline{B})$ which renders as «$x \in \overline{B}\land x\in(\overline{A}\cup \overline{B})$». Everyone wins.
1d
comment Nine plus ten really does equal 21…
Sure, you can add nine plus ten and get a purple water buffalo if you use the right method, but what does it have to do with mathematics?
1d
comment let s be a set with N elements and A1,…,A101 be 101 (possibly not disjoint) subsets of S
I regret that your answer didn't get more upvotes, because when I saw it I thought you had given exactly the right amount of hint. I just wanted to let you know I had liked it.
1d
comment Studying math all day and really young
On the other hand, Paul Erdős said “You know, all of these rules that may be completely correct for normal people, make no sense for prodigies. To say that Bach should pay any attention to how he was socially adjusted is just a bad joke.”
2d
comment let s be a set with N elements and A1,…,A101 be 101 (possibly not disjoint) subsets of S
How to format mathematics on this site
2d
comment Red-Black tree - “Insert-Delete”
Have you read the Wikipedia article about it? It might be less confusing than your notes. Also, it might be helpful if you can find a description of red-black trees that makes the isomorphism with 2-3 trees explicit; they are really the same data structure, with the red/black coloring used to represent a 2-3 tree as a binary tree.
2d
comment Coproduct of groups
No, not in general, but that is a theorem of group theory, not of category theory.
2d
comment Are there any examples of non-computable real numbers?
"Sufficient" is not a subjective term; it is a mathematical term of art with a specific technical meaning.
2d
comment Show that for each $p \in P(n)$, the set $A(p) = \{x \mid p(x) = 0\}$ is countable
Isn't there a theorem of algebra that if $p\in P_n$ then $\{x \mid p(x) = 0\}$ has at most $n$ elements?
2d
comment Show that for each $p \in P(n)$, the set $A(p) = \{x \mid p(x) = 0\}$ is countable
You said “$P(n)$” in two places and “$P_n$” in two places. Did you mean those to be all the same?