Constructivist Foundations 7 (2):126-130 (2012)
Context: The infinite has long been an area of philosophical and mathematical investigation. There are many puzzles and paradoxes that involve the infinite. Problem: The goal of this paper is to answer the question: Which objects are the infinite numbers (when order is taken into account)? Though not currently considered a problem, I believe that it is of primary importance to identify properly the infinite numbers. Method: The main method that I employ is conceptual analysis. In particular, I argue that the infinite numbers should be as much like the finite numbers as possible. Results: Using finite numbers as our guide to the infinite numbers, it follows that infinite numbers are of the structure w + (w* + w) a + w*. This same structure also arises when a large finite number is under investigation. Implications: A first implication of the paper is that infinite numbers may be large finite numbers that have not been investigated fully. A second implication is that there is no number of finite numbers. Third, a number of paradoxes of the infinite are resolved. One change that should occur as a result of these findings is that “infinitely many” should refer to structures of the form w + (w* + w) a + w*; in contrast, there are “indefinitely many” natural numbers. Constructivist content: The constructivist perspective of the paper is a form of strict finitism
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
Similar books and articles
Counting Systems and the First Hilbert Problem.Yaroslav Sergeyev - 2010 - Nonlinear Analysis Series A 72 (3-4):1701-1708.
Numerical Computations and Mathematical Modelling with Infinite and Infinitesimal Numbers.Yaroslav Sergeyev - 2009 - Journal of Applied Mathematics and Computing 29:177-195.
Negative, Infinite, and Hotter Than Infinite Temperatures.Philip Ehrlich - 1982 - Synthese 50 (2):233 - 277.
Infinite Chains and Antichains in Computable Partial Orderings.E. Herrman - 2001 - Journal of Symbolic Logic 66 (2):923-934.
Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor's Theory of Infinite Number Inevitable?Paolo Mancosu - 2009 - Review of Symbolic Logic 2 (4):612-646.
A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.
Added to index2009-01-28
Total downloads191 ( #23,256 of 2,177,988 )
Recent downloads (6 months)16 ( #18,976 of 2,177,988 )
How can I increase my downloads?