**Volume 7 · Number 2**· Pages 126–130

Download the full text in

PDF (305 kB)

## Abstract

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.

Key words: Cantor, infinite number, infinity, ordinals, infinite distance

## Citation

Gwiazda J. (2012) On infinite number and distance. Constructivist Foundations 7(2): 126–130. http://constructivist.info/7/2/126

Export article citation data: Plain Text · BibTex · EndNote · Reference Manager (RIS)

## Similar articles

## References

## Comments: 0

To stay informed about comments to this publication and post comments yourself, please **log in** first.