#### Date of Award:

5-1964

#### Document Type:

Thesis

#### Degree Name:

Master of Science (MS)

#### Department:

Mathematics and Statistics

#### Advisor/Chair:

Neville C. Hunsaker

#### Abstract

This paper is based on Landau's book "Foundations of Analysis" which constitutes a development of the number system founded on the Peano axioms for natural numbers. In order to show mastery of the subject matter this paper gives a somewhat different organization of material and modified or more detailed proofs of theorems. In situations where proofs become rather routine re pet it ions of previously noted techniques the proofs are omitted. The following symbols and notation are used. Natural numbers are denoted by lower case letters such as a,b,c, ... x,y,z. Sets are denoted by upper case letters such as M, N, ... X, Y, Z. If a is an element of M, this will be written atM, The denial of this is written at M. The symbol 3 /x is read "There exists an unique x". If x and y are names for the same number we write x=y. It is assumed that the relation= is an equivalence relation; i.e., (1) x=x, (2) if x=y, then y=x, (3) u x=y and y=z, then x=z. Throughout this paper there will be no special attempt to distinguish between the name of a number and the number itself. For example, the phrase" if xis a number" will be used in place of "if x is the name of a number."

#### Checksum

9d5106d92cd60c759e36893177e47919

#### Recommended Citation

Olsen, Janet R., "A Development of the Number System" (1964). *All Graduate Theses and Dissertations*. 6770.

https://digitalcommons.usu.edu/etd/6770

#### Included in

Number Theory Commons, Numerical Analysis and Computation Commons, Other Mathematics Commons

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