2022-04-23 13:26:53 +01:00
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---
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tags:
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2022-09-06 13:26:44 +01:00
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- set-theory
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- theorems
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2022-04-23 13:26:53 +01:00
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---
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2024-10-18 20:00:02 +01:00
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# Axioms of set theory
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2024-02-02 15:58:13 +00:00
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The basic notions of set theory are defined in
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[Basic properties of sets](Basic%20properties%20of%20sets.md). There we
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introduced a formal syntax that will be utilised to define the axioms. For easy
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reference:
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2022-04-23 13:26:53 +01:00
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- variables $a,b,c,...$ to range over sets
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- variables $x,y,z$ to range over ordinary objects as well as sets.
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## Axiom of Extensionality
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2024-02-02 15:58:13 +00:00
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Sets which contain the same members are the same set. If sets A and B contain
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the same elements then A = B.
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$$\forall a \forall b [\forall x (x \in a \longleftrightarrow x \in b) \rightarrow a =b]$$
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2022-12-04 16:00:04 +00:00
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2024-02-17 11:57:44 +00:00
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[link to test](beta.md)
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