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Title of Paper: Infinity in Set Theory: Beyond Human Comprehension
In examining Kurt Godel’s and Georg Cantor’s theories in set theory, we arrive at the finding that infinity is more than a mathematical or philosophical concept, it is beyond human comprehension; due to set theory having circular arguments, the instance of elements existing simultaneously, and how limits can be understood as unlimited, the idea of infinity cannot be fathomed by human cognition.
1st paragraph: Background on Godel and Cantor’s theories of infinity.
2nd paragraph: The integration of their theories—what does it make? Uncertainty.
3rd paragraph: Why infinity is beyond human comprehension:
– mathematical theories are circular
– simultaneous elements
– how limits tend to be unlimited
Topic 1: Mathematical Theories are Circular
1st paragraph: Examine Cantor’s hierarchy of aleph numbers.
2nd paragraph: Examine Godel Incompleteness Theorem.
3rd paragraph: How having no hierarchy, no incompleteness leads to not knowing.
Topic 2: Simultaneous Elements
1st paragraph: Importance of dual systems.
2nd paragraph: Exclusions and inclusions of elements.
3rd paragraph: Variables are not fixed and leads to not knowing.
Topic 3: Limits Tend to Be Unlimited
1st paragraph: Misconception about there being more than one limit.
2nd paragraph: The infinite’s limit.
3rd paragraph: How can there be limits?
1st paragraph: Summary
2nd paragraph: Afterthought: Can the information presented in this essay about debunking infinity affect the current state of set theory?
Cantor’s Continuum Hypothesis
Godel’s Incompleteness Theorem
Amir D. Aczel (2001).The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity.
Listing one: Meditation: personal infinity.
Listing two: Infinity in our everyday lives.
Listing three: What creative writers have written about infinity as it corresponds to this paper.