Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness of the Leibniz Field and Rigorousness of Infinitesimal
  Calculus   We present a characterization of the completeness of the field of real
numbers in the form of a \emph{collection of ten equivalent statements}
borrowed from algebra, real analysis, general topology and non-standard
analysis. We also discuss the completeness of non-Archimedean fields and
present several examples of such fields. As an application we exploit one of
our results to argue that the Leibniz infinitesimal calculus in the
$18^\textrm{th}$ century was already a rigorous branch of mathematics -- at
least much more rigorous than most contemporary mathematicians prefer to
believe. By advocating our particular historical point of view, we hope to
provoke a discussion on the importance of mathematical rigor in mathematics and
science in general. We believe that our article will be of interest for those
readers who teach courses on abstract algebra, real analysis, general topology,
logic and the history of mathematics.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics