Some Critical Notes on the Cantor Diagonal Argument

Abstract

This paper critically examines the Cantor Diagonal Argument (CDA) that is used in set theory to draw a distinction between the cardinality of the natural numbers and that of the real numbers. The CDA is discussed here using a consensus from the forms found in a range of recent ly published sources. Four points critical of the CDA are raised that cast doubts on its validity and general applicability. Also, contrary to the conclusion conventionally drawn from the CDA, it is found possible to set up a one-to-one correspondence between the natural numbers and the real numbers. Finally, some comments are made on the concept of “ infinity ” , pointing out that to consider this as an entity is a category error, since it simply represents an absence, that is, the absence of a termination to a process.