Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The strange properties of the infinite power tower   In this article we investigate some "unexpected" properties of the "Infinite
Power Tower". \[y = f(x) = {x^{{x^{{x^{{x^
{\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu
  \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} }}}}}}}\] The material
collected here is also intended as a potential guide for teachers of
high-school/undergraduate students interested in planning an activity of
investigative mathematics in the classroom, where the knowledge is gained
through the active, creative and cooperative use of diversified mathematical
tools (and some ingenuity). The activity should possibly be carried on with a
laboratorial style, with no preclusions on the paths chosen and undertaken by
the students and with little or no information imparted from the teacher's
desk. The teacher should then act just as a guide and a facilitator. The
mathematical requisites to follow this path are: functions, properties of
exponentials and logarithms, sequences, limits and derivatives. The topics
presented should then be accessible to undergraduate or "advanced high school"
students.

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg