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visits member for 2 years, 6 months
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I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.


1h
comment Can we sort 6 numbers with at most 9 comparison?
possible duplicate of Is it possible to sort an array of 10 elements with 20 comparisons of two elements?
1h
comment Can we sort 6 numbers with at most 9 comparison?
$5! = 120 < 128 = 2^7$.
1h
comment Can we sort 6 numbers with at most 9 comparison?
There are $6!=720$ possible orders for 6 numbers. 9 comparisons only allows you to distinguish $2^9 = 512$ different situations, so it is not enough.
2h
comment context free grammar that describes even numbers
That looks okay. It is also possible to write a regular (or context-free) grammar for binary numerals that are multiples of 3; you may enjoy trying to find one.
3h
comment Counting partition of set that $i$ and $i+1$ are not in one part
I don't understand your idea. But something must be wrong, because your formula gives the wrong answer for $n=3$.
3h
comment Counting partition of set that $i$ and $i+1$ are not in one part
Perhaps count all the partitions and then subtract those where $i, i+1$ are in the same part, using an inclusion-exclusion argument?
4h
comment Abstract Algebra Book Request
I believe you are thinking of Abel's Theorem in Problems and Solutions: Based on the lectures of Professor V.I. Arnold, by V.B. Alekseev. I give this book an enthusiastic thumbs-up, although I can't say anything more concrete, not having looked at it in several years.
5h
comment Proof a $2^n$ by $2^n$ board can be filled using L shaped trominoes and 1 monomino
Thanks. That is why I referred to the extra square as a "chosen" square. You can choose it to be any square you like.
19h
comment Tiling squares with L-Trominoes
All such squares have an edge length which is a aum of 6es and 9s, so it suffices to exhibit tilings of the $6\times6 $ and the $9\times 9$ squares.
19h
comment Working out the “best” score based on quantity and ratio
Relevant is this article on How Not to Sort by Average Rating, which discusses a solution given in 1927 by Edwin B. Wilson. Oh, I see from your comment below that this is just what you found. I will leave the link here anyway.
20h
comment Elementary Geometry Nomenclature: why so bad?
The Unix system-level function for opening a file is called open. The reason for the name less is as follows: An earlier command, more, would display a file on the terminal and pause after every page to ask more?, waiting for a keypress before continuing to the next page. But it provided no way to go backwards in the file to view the previous pages. The less command appeared later, and was so named because it was like more but would also go backwards. For people already familiar with more, the name was easy to remember.
20h
comment Best book for topology?
@eric Thank you.
20h
comment Are there counter intuitive interpretations of ZF or ZFC?
@Miguelgondu Yes, the $\in$ symbol is a stylized epsilon.
20h
comment Are there counter intuitive interpretations of ZF or ZFC?
@Miguelgondu Many books about set theory, particularly older ones, use $\epsilon$ to represent set-theoretic membership. For example, see pages 252 and following in General Topology of J.L. Kelley.
20h
comment How many ways are there to color the $H$-shaped tree with $3$ colors such that each color is used exactly twice?
@markoriedel This looks like your department.
23h
comment Follow-Up Help with Truth Tables
The final gate is $\oplus$, not $+$. $+$ means or, but the final gate is exclusive or, which is different.
1d
comment Follow-Up Help with Truth Tables
If you don't know that Karnaugh map technique, just make a truth table for $A+\bar AB$ and see if you recognize it as being the same as the truth table of a simpler expression. I don't understand what you are asking when you say “does that relate to the boolean terms”.
1d
comment PDA and Some language Grammar inference
No, I will not do your homework for you.
1d
comment Product in the category of pointed sets..
If you don't know what a coproduct looks like in $\mathbf{Set}$, you don't know what coproducts are. You won't be able to solve this exercise unless you understand coproducts. So go back to your book and reread the part with basic examples of coproducts until you understand what coproducts look like in $\mathbf{Set}$ and in two other categories. If your book doesn't explain that example and two others, get a different book that does have examples.
1d
comment Follow-Up Help with Truth Tables
You can always write $P\operatorname{xor} Q$ as $P\bar Q+ \bar PQ$. Does that help?