Date of Award

Summer 1947

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)




The following thesis contains an elementary account of the logical foundations of the real number system. A system of numbers such as is used in mathematics is a product of human intelligence. Numbers did not exist in the world until they were supplied by man. The invention of an efficient number system came through a series of gradual changes, and the final development of the number system now used represents one of the greatest accomplishments of mathematicians. The common methods of calculation which are employed in schools at present should not be thought of as the only possible methods that can be used. In fact there are many ways in which adding, subtracting, multiplying and dividing may be carried on and thought of, and it is altogether probable that still more efficient methods and their theoretical explanations will be discovered and devised for the schools of the future. It has been my purpose to give a general exposition of the abstract, formal point of view developed during the last seventy years. The thesis is by no means an exhaustive treatment of the number system, but concerns itself with the more important fundamental concepts of the number system confronting the average college mathematics major.