10,786 reputation
2252
bio website vyznev.net
location Helsinki, Finland
age
visits member for 3 years, 5 months
seen 22 hours ago

I'm a PhD student in biomathematics, working on stochastic individual-based models of evolution in spatially structured populations. My other interests include cryptography, programming games and puzzles, photography and graphic design.

I started programming (in AmigaBASIC) when I was 10 years old. Nowadays, I'm most comfortable using Perl, C and JavaScript. I know Java and PHP too, but I can't really say I like them. I also know some Python, but not as much as I'd like.


CC-Zero Please consider any (original) code I post to Stack Overflow and other Stack Exchange sites to be released under CC-Zero unless stated otherwise. You may do whatever you want with it and don't have to credit me in any way, although of course that would be nice.


I'm the main author and maintainer of the Stack Overflow Unofficial Patch (SOUP), a user script for browsers with GreaseMonkey-compatible user script support (Firefox, Chrome, Opera, possibly Safari) that fixes or works around a number of outstanding issues with the Stack Exchange user interface.

I tend to answer a lot more questions than I ask. Some answers I'm rather proud of:


1d
awarded  Explainer
Sep
28
revised Definition of factor - Is n a factor of n?
edited body; edited tags
Sep
28
answered Definition of factor - Is n a factor of n?
Sep
28
awarded  Nice Answer
Sep
27
answered I can't understand logical implication
Sep
25
comment An easy inequality?
Given the symmetry of the problem, and the fact that all the operations involved ($x\to x^3$, $x\to1/x$, $(x,y,z)\to x+y+z$) are fairly simple and monotone, one would generally expect the minimum to be either on the symmetry axis (i.e. where $a=b=c=\sqrt[3]{15/3}$) or as far away from it as possible (i.e. at $a=b=0$, $c=\sqrt[3]{15}$, assuming that all three variables must be non-negative). A natural approach, then, would be to try both, see which one yields the smaller sum of reciprocals, and then see if you can prove that the sum cannot get smaller than that.
Sep
24
awarded  Autobiographer
Sep
24
answered Have I negated the statement “for every prime number $p$, $p+7$ is composite” correctly?
Sep
19
awarded  Nice Answer
Sep
18
revised Can I cancel out quotient function safely?
fix typo ("exact" -> "except")
Sep
18
revised What functions satisfy this functional equation?
if (f, g) is a solution, then so is (f+c, g)
Sep
18
answered What functions satisfy this functional equation?
Sep
10
comment Can a function be applied to itself?
@HelloGoodbye: In standard set theory, yes they are, by the axiom of extensionality. (While you can, sort of, do set theory without extensionality, things get even muddier than just without foundation. Basically, it gets really hard to define anything uniquely, if you can't be sure that two things with exactly the same properties are really the same thing.)
Sep
10
comment Can a function be applied to itself?
Anyway, in some set theories without foundation, you can have functions that belong to their own domain. Even if such functions are allowed, though, self-referential definitions can be tricky. For example, consider the functions $$f(x) = \begin{cases} 1 & \text{if } x = f \\ 0 & \text{otherwise,} \end{cases} \quad g(x) = \begin{cases} 1 & \text{if } x = g \\ 0 & \text{otherwise} \end{cases}$$ defined on some domain known to include both $f$ and $g$; is $f = g$ or not? Absent additional axioms or assumptions, I believe either possibility should be consistent with ZF minus foundation.
Sep
10
comment Can a function be applied to itself?
@HelloGoodbye: In set theory, a function always has a set, called its domain, on which it it defined (and standard ZF set theory does not allow a function to be defined on "the set of all sets", because no such set exists in ZF). The axiom of foundation implies that no function can be part of its own domain. Of course, you're still free to define a function $f$ as above on some domain that doesn't include $f$, but then the definition just becomes equivalent to $f(x) = 0$ for all $x$.
Sep
9
comment Can rational numbers have decimals?
In fact, the square root of a non-square integer is never rational (and the square root of a rational number is never rational unless the numerator and denominator, in reduced form, are both squares). This is easy enough to show in the contrapositive: the square of every rational number $a/b$ can be written as $a^2/b^2$, where $a^2$ and $b^2$ share no common factors, and $a^2/b^2$ is therefore in reduced form.
Aug
29
reviewed Approve suggested edit on Safe with $12 \times 10^6$ combinations? How is it possible?
Aug
29
comment Does this weird sequence have a limit?
@Javier: Just to answer an old question, no it doesn't. If the real-valued sequence converged to some $x \in \mathbb R$, then for any $\epsilon>0$, there would have to be some $k_0$ such that, for all $k>k_0$, $a_k\in[x-\epsilon,x+\epsilon]$. As long as we can choose an $\epsilon>0$ such that each $a_k$ has a non-zero probability of not belonging to $[x-\epsilon,x+\epsilon]$ (i.e. as long as the probability distribution is not concentrated at $x$), the conclusion still follows.
Aug
29
comment Is a dense subset of the plane always dense in some line segment?
@Asaf: I know this is a very old post, but since you said you'd get back to it... Anyway, I went over it again, and I'm fairly sure there's no DC (or even ACω) used here: all the choices that need to be made are from sets of the form $[a, b) \setminus \{x_1, x_2, \dotsc, x_n\}$, and the lemma above singles out a specific element $x = (x_1 + x_2)/2$ for each such set.
Aug
28
comment What is the average of no numbers?
Under IEEE 754, the result of $\dfrac{\pm0}{\pm0}$ is $\rm NaN$, not $\pm\infty$.