Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Where Infinitesimals Come From ..   The presence of infinitesimals is traced back to some of the most general
algebraic structures, namely, semigroups, and in fact, magmas, [1], in which
none of the structures of linear order, field, or the Archimedean property need
to be present. Such a clarification of the basic structures from where
infinitesimals can in fact emerge may prove to have a special importance in
Physics, as seen in [4-16]. The relevance of the deeper and simpler roots of
infinitesimals, as they are given in Definitions 3.1 and 3.2, is shown by the
close connection in Theorem 4.1 and Corollary 4.1 between the presence of
infinitesimals and the non-Archimedean property, in the particular case of
linearly ordered monoids, a case which, however, has a wide applicative
interest.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga