Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Methodology of Numerical Computations with Infinities and Infinitesimals   A recently developed computational methodology for executing numerical
calculations with infinities and infinitesimals is described in this paper. The
developed approach has a pronounced applied character and is based on the
principle `The part is less than the whole' introduced by Ancient Greeks. This
principle is used with respect to all numbers (finite, infinite, and
infinitesimal) and to all sets and processes (finite and infinite). The point
of view on infinities and infinitesimals (and in general, on Mathematics)
presented in this paper uses strongly physical ideas emphasizing interrelations
holding between a mathematical object under the observation and tools used for
this observation. It is shown how a new numeral system allowing one to express
different infinite and infinitesimal quantities in a unique framework can be
used for theoretical and computational purposes. Numerous examples dealing with
infinite sets, divergent series, limits, and probability theory are given.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci