Combining Texts
Ideas for
'Monadology', 'Infinity: Quest to Think the Unthinkable' and 'The Roots of Reference'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
11 ideas
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859
|
A set is 'well-ordered' if every subset has a first element [Clegg]
|
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857
|
Set theory made a closer study of infinity possible [Clegg]
|
10864
|
Any set can always generate a larger set - its powerset, of subsets [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872
|
Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875
|
Pairing: For any two sets there exists a set to which they both belong [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876
|
Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878
|
Infinity: There exists a set of the empty set and the successor of each element [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877
|
Powers: All the subsets of a given set form their own new powerset [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879
|
Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871
|
Axiom of Existence: there exists at least one set [Clegg]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874
|
Specification: a condition applied to a set will always produce a new set [Clegg]
|