id: 06644850
dt: j
an: 2016f.00026
au: Štiberová, Dušana; Tkačik, Štefan
ti: Galileo’s thoughts on infinity. (Galileov pohl’ad na nekonečno.)
so: Obz. mat. fyz. inform. 45, No. 1, 13-24 (2016).
py: 2016
pu: PROTONIT s.r.o., Nitrianske Hrnčiarovce
la: SK
cc: A30 E60
ut: infinity
ci:
li:
ab: Summary: The theory of sets, founded by George Cantor (1845‒1918),
systematically deals with the notion of infinity. Observe that
mathematical studies of infinity and related paradoxes by Bernard
Bolzano (1781‒1848) are of an earlier vintage. But the trailblazer in
this area is Galileo Galilei (1564‒1642), the founder of modern
natural science. The goal of our article is to brush up Galileo’s
revolutionary and modern ideas on infinity. In his treatise {\it
Discorsi e dimostrazioni matematiche intorno a due nuove scienze},
published in 1638, Galileo discussed ways how to compare the size of
infinite sets, the bijection between points of intervals with different
lengths, and the equality of areas of an interval and a single point.
He studied other paradoxes of infinity pointing against the
Aristotle’s maxim the whole is greater than the part. Galileo’s
ideas can serve as an interesting complement to high school
mathematics.
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