Results 231 to 240 of about 250,870 (282)

Logic of Actual Infinity and G. Cantor's Diagonal Proof of the Uncountability of the Continuum

, 2004
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Analysis without actual infinity

Journal of Symbolic Logic, 1981
AbstractWe define a first-order theory FIN which has a recursive axiomatization and has the following two properties. Each finite part of FIN has finite models. FIN is strong enough to develop that part of mathematics which is used or has potential applications in natural science.
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Descriptive definitions of potential and actual infinities

Kybernetes, 2008
PurposeThe paper's purpose is to analyze the concepts of potential and actual infinities.Design/methodology/approachThe exploration and research on potential and actual infinities generally touch on many disciplines, such as philosophy, logic, computer science, mathematics, etc.
Zhu, Wujia, Lin, Yi, Gong, Ningsheng, Du, Guoping   +3 more
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Kant’s Mereological Account of Greater and Lesser Actual Infinities

Archiv für Geschichte der Philosophie, 2021
Abstract Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude.
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The conceptual evolution of actual mathematical infinity

Educational Studies in Mathematics, 1991
The different stages in the conceptual evolution of actual infinity are analyzed. We show how this concept occurs in high-school students at a prior, or at best, at the same level, as in Bernard Bolzano's conceptualization (as defined in his work The Paradoxes of Infinity).
E. Luis, A. Moreno, Guillermina Waldegg
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Consistency and Representations: The Case of Actual Infinity

Journal for Research in Mathematics Education, 1999
In this article we demonstrate how research-based knowledge about students' incompatible solutions to various representations of the same problem could be used to raise their awareness of inconsistencies in their reasoning. In the first part of the article we report that students' decisions as to whether 2 given infinite sets have the same number of ...
Pessia Tsamir, Dina Tirosh
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A Flawed Argument Against Actual Infinity in Physics

Foundations of Physics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Actual and Potential Infinities

2016
Historically, the most popular theory of the impossible infinite is the one handed down by Aristotle: that infinity can only be potential, never actual.1 What does this mean? Here are two helpful remarks from Aristotle’s discussion of the infinite: A quantity is infinite if it is such that we can always take a part outside what has already been taken.
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