Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On flexible sequences   In the setting of nonstandard analysis we introduce the notion of flexible
sequence. The terms of flexible sequences are external numbers. These are a
sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot )
$} notation for functions, and have algebraic properties similar to those of
real numbers. The flexibility originates from the fact that external numbers
are stable under some shifts, additions and multiplications. We introduce two
forms of convergence, and study their relation. We show that the usual
properties of convergence of sequences hold or can be adapted to these new
notions of convergence and give some applications.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph