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Jan
10
comment Why Riemann hypothesis and not Riemann's conjecture
Probably "Riemann's hypothesis" is just older terminology.
Jan
10
comment Showing that an iterative method solves a particular system
@Variable The idea is to show that when $\theta$ is chosen to make it converge for all $x_0$, it converges to a solution to $Ax=b$.
Jan
9
comment Showing that an iterative method solves a particular system
@Variable An old exercise sheet from a numerical analysis class which covered the Jacobi, Gauss-Seidel, and SOR methods. Maybe we really were just intended to see that the solution to $Ax=b$ is $(1, 1)$ and then plug that into the fixed point equation.
Jan
9
comment Proof that $A^{-1}=adj(A)/|A|$
@SanchayanDutta As you do more and more of your own mathematics, this sort of thing bothers you less and less. When working on a difficult problem, very often the solution will just pop into your head after a long time thinking about it, seemingly out of the blue. Other times you find a solution in a more natural way, but then a radical and more elegant reformulation of it comes into your head out of nowhere. If that can happen to you, just imagine the kinds of crazy ideas that would appear when the best minds in history spend their lives working on problems over thousands of years.
Jan
9
comment Maximal tiling without any 3-in-a-rows
@PeterTaylor Oh, I see, I thought this was basically a sort of infinite tic tac toe, with no three-in-a-rows of either kind allowed. Well, I'll leave my answer up. Probably with some more case analysis a similar method would yield an answer to this question.
Jan
9
answered Maximal tiling without any 3-in-a-rows
Jan
9
comment Maximal tiling without any 3-in-a-rows
I've thought about this problem before. There turns out to be only one way to do it (optimal or non-optimal, and even if you allow non-periodic solutions), not counting obvious symmetries like rotations, flips, and swapping 0 and 1.
Jan
9
comment Showing that an iterative method solves a particular system
@Variable Fixed.
Jan
8
comment In a general definition, a sequence starts at zero or at one?
If you intend to count the sequence in any way, start at $1$, that way $x_1, x_2, ... x_n$ consists of exactly $n$ elements. If the sequence is defined by a recurrence $x_{n+1} = f(x_n)$, it's often nicer to start at $0$, that way an element's index tells you how many times it's had $f$ applied to it.
Jan
8
comment Is it possible to solve this?
Fixing $x$, this can obviously only be true for finitely many $n$. If it's true for $k$ distinct values of $n$, then we have $e^x=\sum x^n/n!\geq ke$, so $k$ is bounded above by $e^{x-1}$. That's all I've got off the top of my head. You might also study the monotonicity of the sequence $x^n/n!$ to get a better picture of the situation.
Jan
8
revised Is it possible to solve this?
edited tags
Jan
8
asked Showing that an iterative method solves a particular system
Jan
8
comment Finding the function that would describe this:
@Asta If you do decide to do post more details though, you should definitely do so as a new question.
Jan
8
comment Finding the function that would describe this:
@Asta Well, we can hardly give satisfying answers if you don't post all the parameters. There are infinitely many functions that will generate the numbers 10, 5 and 2. You should post the full list of numbers. If it's a finite list, then I guarantee "the" answer won't involve tetration, and if it's infinite, you should explain where you're getting the numbers.
Jan
7
comment Odd Graph Problem
So, to reformulate: let $G$ be a connected graph. You want a lower bound on $\deg(x) + \deg(y)$, as $x$ and $y$ range across all pairs of distinct vertices of $G$?
Jan
7
answered Finding the function that would describe this:
Jan
7
comment Finding the function that would describe this:
@CommonerG Writing $f_1(x) = \frac 6 {x + 1}$, we get $f_1(0) = 6, f_1(1) = 3$ and $f_1(2) = 2$. Same for the second pair of sequences.
Jan
7
comment Why using determinant equal to zero
A good example for why determinants are useful despite the fact that Gauss' algorithm already provides a way to tell when a system has a non-unique solution. Imagine trying to solve for $u_1$ and $u_2$ from the first equation, not knowing what the $x_i$ might be!
Jan
7
revised The “Set's theory” error!
edited tags
Jan
7
comment The “Set's theory” error!
What does the "==" sign mean? That the two sides have the same truth value?