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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Research Questions
1.4 Significance of the Study
1.5 Definition of Key Terms

Chapter 2: Literature Review
2.1 Overview of p-adic Numbers
2.2 Historical Development of p-adic Numbers
2.3 Properties of p-adic Numbers
2.4 Applications of p-adic Numbers

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Limitations of the Study

Chapter 4: Discussion of Findings
4.1 Analysis of p-adic Number Construction
4.2 Examination of Properties of p-adic Numbers
4.3 Comparison of p-adic Numbers to Real Numbers
4.4 Implications of Findings

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Recommendations for Future Research

Brief Overview:

The thesis “Constructing p-adic numbers and studying their properties” delves into the fascinating world of p-adic numbers, a concept in mathematics that extends the notion of numbers to include infinite decimals with respect to a given prime number p. This thesis aims to explore the construction of p-adic numbers, their unique properties, and their applications in various fields.

Chapter one provides an introduction to the study, outlining the background, problem statement, research questions, significance, and key terms. Chapter two presents a comprehensive literature review on p-adic numbers, discussing their history, properties, and applications. Chapter three details the research methodology, including design, data collection methods, analysis techniques, and limitations.

Chapter four delves into the discussion of findings, analyzing the construction of p-adic numbers, exploring their properties, comparing them to real numbers, and discussing the implications of the findings. Finally, chapter five concludes the thesis, summarizing the findings, drawing conclusions, and providing recommendations for future research in the field of p-adic numbers.

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