Combining Texts
Ideas for
'The Roots of Reference', 'What are Sets and What are they For?' and 'What Required for Foundation for Maths?'
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10 ideas
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240
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The empty set is something, not nothing! [Oliver/Smiley]
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14241
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We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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14239
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The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
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14242
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Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243
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The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17795
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Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry]
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17796
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There is a semi-categorical axiomatisation of set-theory [Mayberry]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
17800
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The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
17801
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The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
17803
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Limitation of size is part of the very conception of a set [Mayberry]
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