Short reports
ScienceAsia (): 396-399 |doi:
10.2306/scienceasia1513-1874...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 1246 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
|
