The infinite-sequences tag has no wiki summary.

**-2**

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87 views

### Is it possible to list $\mathbb{Q}$ so that the result set to be a monotoic sequence? [migrated]

Let $\mathbb{Q}$ be the set of rational numbers. Is it possible, relabeling if needed, to list $\mathbb{Q}$ such that the result set to be a monotonic sequence? If not, why? If it is true, where is ...

**3**

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**1**answer

42 views

### Complete classification of complexity classes / infinite approaching sequences

http://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities
For complexity as seen in the above link, complexity classes can be log, polynomial, exp, or composition of any of these ...

**2**

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**1**answer

113 views

### Is there a dense rational sequence of positive separation?

Let us consider the set $\ell_\neq$ of bounded sequences of unequal real terms. We use the following descriptions. A sequence $x=(x_0,x_1,...)\in\ell_\neq$ is dense if, for all $\varepsilon>0$, ...

**0**

votes

**1**answer

160 views

### Lemma about infinite sequences we are hoping is true [closed]

Given N infinite sequences of non-negative integers, some of which diverge to infinity, must there exist two steps i, j in which $x_i \leq x_j$ for all sequences x?

**1**

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83 views

### Bound a sum of a serie defined by a recursive integer function

I'm using a recursive function $f: \mathbb{N} \rightarrow \mathbb{N}$, that is defined as
\begin{equation}
f(n)=\lceil \log(f(n-1)) \rceil +f(n-1)
\end{equation}
where $f(1)=F\in \mathbb{N}$, and ...

**2**

votes

**1**answer

109 views

### Iterated projections in Hilbert spaces

Let $E$ be an Hilbert space and $F, G$ two subspaces such that $F \cap G =\{0\}$. Let $(x_n)$ be the sequence of iterated orthogonal projections: $x_0 \in F$, $x_1$ is the orthogonal projection of ...

**0**

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120 views

### Greedy sequences without k-term arithmetic progressions

If $S_k$ is the greedy sequence with no length-k arithmetic subsequence, (ie $S_3$ = A003278 , $S_4$ = A005837 , $S_5$ = A020655 ), is it guaranteed that any other sequence $a$ with no length-k ...

**0**

votes

**2**answers

180 views

### sequence, such that sum of any combinations in the sequence does not equal another [closed]

Hi,
Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence.
...

**-2**

votes

**1**answer

190 views

### How to work with infinite random graph(s) ?

Hi,
In the case where we are dealing with an infinite random graph (RG with infinite nodes).
How do we model/work with notions like degrees, degree distribution ? How are they defined ?
Thanks!

**1**

vote

**2**answers

272 views

### sum of infinite series

Given the complex variable $x$, complex constant $c$, and integer number $r$. I want to solve the equation:
$\sum_{k=1}^{\infty}\frac{e^{kx}}{k^r}=c$. I was thinking that if there is a formula or ...

**1**

vote

**2**answers

309 views

### Is it necessary that gcd > 1 of an infinite set? [closed]

Consider an infinite set $S$, of positive integers.
If all the finite subsets of $S$ have GCD $>$ $1$, is it necessary that the GCD of $S$ is greater than $1$ as well?

**2**

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**2**answers

393 views

### References for the result that $\sqrt{n}$ is equidistributed mod 1

It is not difficult to show (even without Weyl criterion) that the sequence $\sqrt{n}$, $n=1,2,\ldots$ is equidistributed mod 1. However, I need a reference to this result. Can you help me? Thanks.

**0**

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**0**answers

268 views

### In a network with N nodes, what is the general formula for computing the propagation of a set of numbers?

I am creating a circular neural network with N nodes. Each node is connected via a send pathway to every other node, and the connection between two nodes has a weight. Any number sent over the ...

**12**

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**1**answer

803 views

### Self-avoiding walk on $\mathbb{Z}$

This one is an unanswered question in Math.SE. I've posted it here because I think it deserves more attention.
How many sequences $\{a_n\}$ exist satisfying:
a) $a_1=0$
b) $\forall k\ge1 $ ...

**3**

votes

**2**answers

371 views

### Ends of topological spaces. Why independent of choice of ascending sequence of compact subsets?

Quoting from http://en.wikipedia.org/wiki/End_(topology):
"Let X be a topological space, and suppose that
K1 ⊂ K2 ⊂ K3 ⊂ · · ·
is an ascending sequence of compact ...

**6**

votes

**1**answer

457 views

### Magic square on an infinite lattice

This question came to me while reading the discussion of magic square in the complex plane with equal integrals along every horizontal, vertical and diagonal "magic square in the complex plane with ...

**0**

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**4**answers

2k views

### Does Cauchy continuity imply uniform continuity? [No.] [on hold]

It is well known that if $X$ is a first countable topological space and $Y$ is a topological space, then $f : X \rightarrow Y$ is continuous iff
$$\forall x \in {\rm map}(\mathbb{N},X),\forall p \in X ...