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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?
Jan
6
comment Proving set property in real analysis
There's almost an algorithm for proving that sets are equal to one another, in basic set theory. If you need to prove that $X=Y$, first prove that $X\subseteq Y$, then prove that $Y\subseteq X$. If you need to prove that $X\subseteq Y$, then write "Let $x\in X$" and try to prove $x$ is in $Y$.
Jan
5
comment Can we assign a number to each theorem stating its complexity?
@PaoloFranchi The notion necessarily has to be relative to a given theory. In a theory in which Fermat's last theorem is an axiom, FLT has a very different complexity than in Peano Arithmetic.
Jan
5
answered Calculations for grid based games
Jan
5
comment Calculations for grid based games
Okay, I see now. So what is it exactly that you want? You want a way of assigning a "difficulty score" to any given initial state of the board? Or a way of fixing a reasonable "target score" for a given board?
Jan
5
comment Calculations for grid based games
What is a "move"? Does the grid start empty and you place objects to create matches..? Or does it start filled and you swap pieces? Is it partially filled and you move the pieces around...? Where do the new items appear when the old ones vanish?
Jan
5
comment Calculations for grid based games
It's not at all clear to me what a "grid game to match items in chains" is. Is this a one player game? Two player? Do you place the items wherever you want? What are the "items"?
Jan
5
answered Reflected rays /lines bouncing in a circle?