Date of Award

Summer 1950

Degree Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)


Mathematical and Statistical Sciences


The object of this monograph is to establish a point system on a line that is continuous. This requires, first of all, that the set of all points on a line on which a scale has been established, and from which the point P, is excluded, form a field with respect to the operations of addition and multiplication, where the operations addition and multiplication are defined. This is the rational field on a line. To make the point system on a line continuous it is necessary to introduce the "irrational points" ; this is done by the assumption of continuity.