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I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.


21h
comment Roots Of Monic Cubic
@theage This comes up all the times in contest problems. See Vieta's formulas. Here is a related problem: Let $p,q,r$ be the three roots of $x^3 + 4x^2 -4x + 1$. Find $p^3+q^3+r^3$.
1d
comment Are there any well known mathematicians who published very little?
If you're going to nominate Christian Goldbach, I can do one better: John Pell, the namesake of Pell's equation, has not one but zero remarkable contributions.
Jul
18
comment Numbers whose digits sum to 7
The idea is to reinterpret the base-10 numerals as if they were base-8 numerals, and doing so will put the elements of $S$ into (almost) one-to-one correspondence with the integers that are multiples of 7. For example, $S$ contains $142$, which corresponds to $142_8 = 98 = 7\cdot14$. it's easy to count multiples of 7, so if it's not too hard to count how many base-8 numerals have a digit sum of 14, 21, 28, etc., then one could subtract those and get the right count for elements of $S$.
Jul
18
comment Numbers whose digits sum to 7
I think I see your point now. Thanks.
Jul
18
comment Numbers whose digits sum to 7
@j.j. I don't see how binary search is going to help either. Suppose I ask you for $S(100)$. What do you search for?
Jul
18
comment Numbers whose digits sum to 7
Perhaps I'm being dense, but I don't see how this helps.
Jul
18
comment Find the 325th term of the series 7,16,25,34…
@TonyK A question worth thinking about perhaps! math.stackexchange.com/questions/870952/…
Jul
18
comment Find the 325th term of the series 7,16,25,34…
@tonyk If OP's characterization is correct, then after 70, one would have 106.
Jul
18
comment Flaw in the proof that a set is countable
This is a common mistake. In fact $S\ne \bigcup_1^\infty A_i$, since elements of $S$ are infinite sequences, while elements of the $A_i$ are finite sequences. The set of all finite sequences is countable, as has been discussed on this site many times. (I haven't found an exact match yet, but these are quite similar: (1)(2))
Jul
17
comment What is the notation for a sub-expression?
The word "subexpression" is commonly used. I suggest that you pick some symbol like $\prec$ or $\lhd$ that resembles a less-than sign and say up front something like "We will write $a\lhd b$ to mean that $a$ is a subexpression of $b$; for example $5\lhd 5\times(3+4)$ and $3+4\lhd5\times(3+4)$." This too is common.
Jul
17
comment Basic Mixture question
I don't understand what a 100% sugar solution is anyway. Wouldn't that be all sugar and no water?
Jul
17
comment Basic Mixture question
Are those fluid ounces or avoirdupois ounces? (This is not a joke; it makes a difference for the answer.)
Jul
17
comment An equation on Catalan number
What is your question?
Jul
16
comment How would you change math notation?
Related: Strangest notation?
Jul
16
comment Calculating a Factorial Base Representation
It is very useful for generating permutations, however. Suppose you want to take an integer $k\in[0,\ldots,n!-1]$ and generate the $k$th permutation of some $n$-set, where the permutations are considered to be in lexicographic order, with the first being $\langle 1,2,\ldots, n-1, n\rangle$, the second being $\langle 1,2,\ldots, n, n-1\rangle$, and the last being $\langle n, n-1, \ldots, 2, 1\rangle$. The factorial-base representation of $k$ is exactly what you need in order to do this.
Jul
15
comment Notation for the smallest number in a set?
I don't think anyone does write “$\displaystyle{\min_{x\in S}}$”. I would more readily believe “$\displaystyle{\min_{x\in S} f(x)}$”. Can you point to a published example of this?
Jul
15
comment Any way to represent number that comes after repeating decimal?
Every element of the sequence has an index in $\{1, 2, 3, \ldots, \omega \}$ because that's the sequence I said I was discussing.
Jul
15
comment Any way to represent number that comes after repeating decimal?
If the sequence is indexed by $\{1, 2, 3, \ldots, \omega\}$, then every position is either an ordinary number, one of $1, 2, 3, \ldots$, or else it's $\omega$. The position $\omega$ is not the next-to-last because it is the very last. None of the positions $1, 2, 3, \ldots $ is next-to-last either. (You tell me why not.) So none of them are next-to-last.
Jul
15
comment Any way to represent number that comes after repeating decimal?
I think this particular question has come up more than once before. The idea of an infinite sequence of 9s followed by an 8 is coherent by itself, but then you can't turn it into a usable number system.
Jul
14
comment Are there any well known mathematicians who published very little?
This edition of the collected works of Bernhard Riemann is 675 pages long. Wikipedia claims “Galois's collected works amount to only some 60 pages.”