82,763 reputation
4111212
bio website henning.makholm.net
location Copenhagen, Denmark
age 41
visits member for 3 years
seen yesterday

I'm a computer scientist by training (Ph.D. in programming language technology, 2003), currently working in industry. Real mathematics is more of a hobby.

In general, don't assume I necessarily know what I'm talking about, unless it's about computer science or formal logic. I dabble in various other fields that I've never taken courses in, mostly just by extrapolating from Wikipedia.


14h
awarded  Nice Answer
Aug
24
comment Necessary and sufficient condition for a directed graph be Eulerian circuit and Hamilton cycle
@jwg: Hmm, yes.
Aug
16
answered Finding $p'(0)$ for the polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$
Aug
15
awarded  Nice Answer
Aug
15
awarded  propositional-calculus
Aug
11
comment Different Forms of the Halting Problem
$\bot$ (pronounced "bottom") means "do not produce any result, enter an infinite loop instead". The most standard halting problem would either be your original or (4). Since they are equally undecidable people don't always care a lot whether they mean one or they other when they say "the" halting problem.
Aug
10
comment When do the sine components of a Fourier series vanish?
When $c_n=c_{-n}$ for all $n$.
Aug
10
comment Why do we assume relatively primes?
@VikramSaraph: Not quite. For example, $7$ is prime, but $(7,14)$ is not $1$.
Aug
10
answered Different Forms of the Halting Problem
Aug
10
revised Strict local extremum without $f'$ “changing signs”
added 68 characters in body
Aug
10
answered Strict local extremum without $f'$ “changing signs”
Aug
10
comment Finding the position at n?
@whyguy: The "single formula" could (for example) be something like $p_n = -2 + A\cos(\frac{\pi}3 n)+B\cos(\frac{\pi}3(n+1))$ for some $A$ and $B$ that you would need to find such that they make $p_0$ and $p_1$ come out right. Not much more enlightning than the table.
Aug
10
comment Finding the position at n?
@whyguy: You can write it down as a single formula, but it will be much less readable than "take the $(n\bmod 6)$th entry in this table", and also more difficult to work with without (as far as I can see) having any real benefit to offset that.
Aug
10
comment Finding the position at n?
@whyguy: Yes, in general. But see Thomas Andrews's answer -- you don't actually need to find the coefficients explicitly in this case.
Aug
10
comment Finding the position at n?
Yes, but you can just raise them to powers and solve for the coefficients in the usual way anyway -- or, as Thomas Andrews did, notice that they're roots of unity so the corresponding terms in the solution repeat cyclically.
Aug
10
comment Finding the position at n?
Better than my approach. It doesn't look like a shortcut to solve for the $a_i$s first, but it is ...
Aug
10
answered Finding the position at n?
Aug
10
comment Finding the position at n?
Do you know (or are you supposed to know) any general procedure for solving linear recurrences?
Aug
10
comment the infinity axiom depends on axiom of regularity
How would you know that $a^+\not\subset a$ if not as a consequence of Regularity? There are (if ZF is consistent) models of ZFC$-$Reg that contain things such as $a=\{a\}$; in this case plainly $a^+=a$.
Aug
10
comment Is it possible to prove that $x=\{x\}$ is false in ZF system?
@user46944: The axiom of regularity claims that $B$ has an element that is disjoint from $B$. But the only element of $B$ is $A$, which is not disjoint from $B$ -- namely, $A\cap B=\{A\}$ is not empty.