1 citations · 1 across the 5 of their papers we have counts for
5 papers
Bernard Bolzano: from Topological to Arithmetical Continuum and Back Again
Kateřina Trlifajová
Although Bolzano's concept of the continuum has gradually evolved, the basis remained the same: the continuum as an infinite class of points arranged in such a way that the so-call…
Theological reasoning of Cantor's set theory
Kateřina Trlifajová
Discussions surrounding the nature of the infinite in mathematics have been underway for two millennia. Mathematicians, philosophers, and theologians have all taken part. The basic…
Sizes of Countable Sets
Kateřina Trlifajová
The paper introduces the notion of the size of countable sets that preserves the Part-Whole Principle and generalizes the notion of the cardinality of finite sets. The sizes of nat…
Bolzano and the Part-Whole Principle
Kateřina Trlifajová
The embracing of actual infinity in mathematics leads naturally to the question of comparing the sizes of infinite collections. The basic dilemma is that the Cantor Principle (CP),…
Bolzano's measurable numbers: are they real?
Steve Russ, Kateřina Trlifajová
During the early 1830's Bernard Bolzano, working in Prague, wrote a manuscript giving a foundational account of numbers and their properties. In the final section of his work he de…