| Home  | About ScienceAsia  | Publication charge  | Advertise with us  | Subscription for printed version  | Contact us  
Editorial Board
Journal Policy
Instructions for Authors
Online submission
Author Login
Reviewer Login
Volume 50 Number 1
Volume 49 Number 6
Volume 49 Number 5
Volume 49S Number 1
Volume 49 Number 4
Volume 49 Number 3
Earlier issues
Volume  Number 

previous article

Short reports

ScienceAsia 35 (2009): 396-399 |doi: 10.2306/scienceasia1513-1874.2009.35.396


A note on the existence of the integers and rationals


Athipat Thamrongthanyalak, Pimpen Vejjajiva*

 
ABSTRACT:     We examine the role of the replacement axiom and the power set axiom in proving the existence of the integers (ℤ) and the rationals (ℚ). We show that without the power set axiom, the replacement axiom is sufficient for the existence of ℤ and ℚ but if both axioms are removed from Zermelo-Fraenkel set theory, then no infinite Cartesian products can be proved to exist and thus the existence of ℤ and ℚ cannot be proved.

Download PDF

20 Downloads 1142 Views


Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

* Corresponding author, E-mail: pimpen@abhisit.org

Received 4 May 2009, Accepted 13 Oct 2009