Combining Texts
Ideas for
'works', 'Set Theory and Its Philosophy' and 'Infinity: Quest to Think the Unthinkable'
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16 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
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A set is 'well-ordered' if every subset has a first element [Clegg]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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Usually the only reason given for accepting the empty set is convenience [Potter]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
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Set theory made a closer study of infinity possible [Clegg]
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Any set can always generate a larger set - its powerset, of subsets [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
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Pairing: For any two sets there exists a set to which they both belong [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
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Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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Infinity: There is at least one limit level [Potter]
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Infinity: There exists a set of the empty set and the successor of each element [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
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Powers: All the subsets of a given set form their own new powerset [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
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Axiom of Existence: there exists at least one set [Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
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Specification: a condition applied to a set will always produce a new set [Clegg]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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Nowadays we derive our conception of collections from the dependence between them [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
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