Recent content by Hurkyl

http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Just in case someone hits this from google (like I did), I have a reference. Buck, in Advanced Calculus, says: Theorem If \int_c^\infty f(x,u) \, du converges to F(x) for all x, a \leq x \leq b, and if f and f_1 = \partial f/\partial x are continuous for a \leq x \leq b, c \leq u < \infty...

It's a precursor to Dixon's method. Python is probably a better choice; it has arbitrary precision integers built-in, and is generally easier to program in.

I can't make sense of your formulae. I think you messed up the typesetting. Also, it may help to use words instead of symbols... especially if you have to improvise to make the symbols.

There is a physical marker: it on the trajectory that was fired from the gun, whereas other electrons aren't. By symmetry it might make sense to say that electron could have been any electron in the universe, however we can still note that it is the same electron that is there is the same...

Er, that proverb usually refers to the situation where people reject using a good solution in favor searching for a mythical best solution -- not the situation where people are using something good and then something better comes along.

Have you seen http://www.irregularwebcomic.net/comic.php?current=203&theme=12&dir=first5 ? Surely you can get some of those ladies to invest in your business?

We can salvage Ray's argument if we can find a real solution for the y's amongst the two-dimensional space of complex solutions. Writing e^{ix} = a + bi, the one complex equation becomes y_1 + (a+ bi) y_2 + (a^2 -b ^2 + 2abi) y_3 = 0 And now we can read off a real solution by inspection: if...

There's no reason to think Det(A + Bi) = 0 should imply Det(A) = 0. As a concrete example, consider the matrix \left( \begin{matrix} 1 & 0 \\ 1 & -1 \end{matrix} \right) which is the real part of the matrix \left( \begin{matrix} 1 & i \\ i+1 & i-1 \end{matrix} \right)

If the density matrix A of the state can be approximately written as a convex combination of the density matrices of pure states: A \approx \sum_{i=1}^n c_i | \psi_i \rangle \langle \psi_i | then this summation remains valid after unitary evolution too. So, it's fair to describe the state...

What does "time of car A" mean, and what does it have to do with the problem?

I bet it's the other way around. :-p

The homogeneous equation (a+b)^3 = (a+c)^3 defines an algebraic curve of degree 3 in the projective plane (with indeterminates a, b, c). So does the homogeneous equation (a+b)^3 = (b+c)^3. Therefore, exactly one of the following two statements is true: The two curves have a common component...

Both number lines are ordered from smallest to largest. So 1 is a colder temperature than -1. *: In the extended sense. I don't think

The usual extended number line looks like this: (-\infty) --- (-1) --- (0) --- (1) --- (+\infty) (where I've rescaled the line so that I can draw it in finite space) However, for the temperature extended number line, it's organized like this instead: (0^+) --- (1) --- (\infty) --- (-1) ---...