Abstract

Lee(2014; 2015) claimed that, in the program of the pre-service school teacher training, real numbers should be defined using the infinite decimal expansion so as to resolve the double discontinuity problem between school and college mathematics. Li(2011) wrote a mathematical paper on the construction of the real numbers via the infinite decimal expansion and supported the argument. On the other hand, Park(2016) analyzed Li's paper and showed that this paper contains the error of circular logic using ‘limit to a real number’. This study shows that Park(2016) misunderstood the introduction of Li's paper and revealed that appropriate axiom must be assumed to avoid the error of circular logic in real number construction. Through this, we resolved the confusion in the studies of Lee(2014; 2015) and Park(2016) and discussed the implications for pre-service school teacher education proposed in each study could be compatible with each other.

Full Text

Published Version

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.