Step by step: Infinite iterative processes and actual infinity

2010 ◽  
pp. 115-142 ◽  
Author(s):  
Anne Brown ◽  
Michael McDonald ◽  
Kirk Weller
Keyword(s):  
Actual Infinity ◽  
Iterative Processes

Meet fractal curves with 1C:MathKit

2020 ◽  
pp. 38-48
Author(s):  
O. M. Korchazhkina
Keyword(s):  
Methodological Approach ◽  
Fractal Curve ◽  
Iterative Processes ◽  
Geometric Figures ◽  
Modern Natural ◽  
Geometric Objects ◽  
Ict Tools ◽  
Subject Areas ◽  
The Subject ◽  
And Mathematics

The article presents a methodological approach to studying iterative processes in the school course of geometry, by the example of constructing a Koch snowflake fractal curve and calculating a few characteristics of it. The interactive creative environment 1C:MathKit is chosen to visualize the method discussed. By performing repetitive constructions and algebraic calculations using ICT tools, students acquire a steady skill of work with geometric objects of various levels of complexity, comprehend the possibilities of mathematical interpretation of iterative processes in practice, and learn how to understand the dialectical unity between finite and infinite parameters of flat geometric figures. When students are getting familiar with such contradictory concepts and categories, that replenishes their experience of worldview comprehension of the subject areas they study through the concept of “big ideas”. The latter allows them to take a fresh look at the processes in the world around. The article is a matter of interest to schoolteachers of computer science and mathematics, as well as university scholars who teach the course “Concepts of modern natural sciences”.

Kant’s Mereological Account of Greater and Lesser Actual Infinities

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Daniel Smyth
Keyword(s):  
Recent Work ◽  
Spatial Representation ◽  
Actual Infinity

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. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others.

scholarly journals On the stability of asynchronous iterative processes

1987 ◽  
Vol 20 (1) ◽  
pp. 137-153 ◽  
Author(s):  
John N. Tsitsiklis
Keyword(s):  
Iterative Processes ◽  
The Stability

Consistency and Representations: The Case of Actual Infinity

1999 ◽  
Vol 30 (2) ◽  
pp. 213 ◽  
Author(s):  
Pessia Tsamir ◽  
Dina Tirosh
Keyword(s):  
Actual Infinity

Optimal iterative processes for root-finding

1972 ◽  
Vol 20 (5) ◽  
pp. 327-341 ◽  
Author(s):  
Richard Brent ◽  
Shmuel Winograd ◽  
Philip Wolfe
Keyword(s):  
Iterative Processes ◽  
Root Finding

scholarly journals TWO TRADITIONS OF THE ACTUAL INFINITY INTERPRETATION

Metaphysics ◽  
2021 ◽  
pp. 47-62
Author(s):  
V. N Katasonov
Keyword(s):  
Rene Descartes ◽  
The Other ◽  
Theory Of Knowledge ◽  
Actual Infinity ◽  
Nicholas Of Cusa ◽  
René Descartes

The article considers two traditions in the interpretation of the actual infinity. One is associated with the name of Nicholas of Cusa, the other with the name of Rene Descartes. It is shown how Nicholas of Cusa within the framework of his idea of the coincidentia oppositorum overcomes the traditional Aristotelian norms of philosophizing, while Descartes puts the finitist ideology at the foundation of both his theology and the theory of knowledge.

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