The Axiomatic Set Theory is an exact discipline, that is a Domain of Mathematics, defined by a set of non-logical axioms, like all formal domains are.
Non-logical axioms forming the domain of Formal Set Theory (Axiomatic Set theory):
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Unrestricted Composition.
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Set identity is membership.
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Order Does not matter.
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Repeats Dont change anything.
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Description Does not matter.
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The union of any sets is a set.
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And a subset is a set.
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A set can have just 1 member.
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A set can have no members.
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A set of sets is a set.
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Sets can contain themselves.
A paradox is a self-contradictory statement or proposition. And Russell’s paradox is a paradox in core logic itself as "is not true of itself" is the linguistic way of thinking about this paradox, in terms of predicates. Using above predicate I can prove that Russell’s paradox is not just a paradox within the Set Theory but a paradox that "just exists," i.e, in core logic.
Summary
Russell’s Paradox demonstrates a contradiction arising in Axiomatic Set Theory. It explores the idea of a set containing all sets that do not contain themselves. It can also be explained in terms of Naive Set Theory. And demonstrated in Linguistics using predicates.
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Start of the series Mathematics - My Research
Final Grade and Comments
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✅ Graded assignment by
rdd13ron July 12th 2025. A
