Title:Infinity: The Continuum Hypothesis
The title should be brief but explain to the reader the focus of the paper.
Introduction
This section should summarize the three strands of the paper and what the reader can expect to learn in this paper. This should be 1-2 paragraphs in length and written after the final paper is composed.
Strand 1: The History of [Your Topic]
- Aristotle (actual and potential infinity)
- Georg Cantor
- One-to-one correspondence
- Continuum hypothesis
- Kurt Gödel
- Paul Cohen
This section should focus on the historical evolution of the chosen topic. Bulleted items may include the most significant aspects of the history of the topic. Each of these may be expanded upon in the Strand 1 paper.
The history of the selected topic should be chronological and focus on the most important aspects of the topics development. It does not need include every contribution.
Strand 2: The Mathematics of [Your Topic]
- One-to-one correspondence
- Cardinality of infinite sets
- Subsets
- Proving or disproving the CH
This section should focus on the mathematical aspects of the topic. Bulleted items may include important formulas, interpretations of proofs, and/or consideration of arguments made by mathematicians. Each of these may be expanded upon in the Strand 2 paper.
The mathematics of the selected topic should first explain any sub-concepts. In this case it is necessary to first discuss cardinality and one-to-one correspondence. Be specific and clear. It may be necessary to use proper mathematical symbols, equations, or formulas in this section to supplement the explanation. Write this section as though the reader does not know about the topic, explaining the topic in detail with supporting evidence.
Part 3:The Real-World Applications of [Your Topic]
- Fractals
- Infinity is highly abstract
- May only be conceivable in your mind
- No true real-world examples exist
- Examples that are used require a certain abstraction
This section should focus on the real-world applications of the chosen topic. Bulleted items may include usages or examples of where the concept is seen. Each of these may be expanded upon in the Strand 3 paper.
Conclusion
In this section, summarize findings. What was interesting? What was unexpected? What did you learn from this research?
References
References should be listed on a separate page, using proper APA formatting.
A variety of sources is encouraged. Use the sources within papers and textbooks as leads for new reading material. Consider textbooks, articles, journals, YouTube videos, websites, etc.
NOTE: Wikipedia is not a proper source to be sited within your paper; however, the resources listed at the bottom of the Wikipedia site may provide a starting place for research.