Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Elements of Set Theory' and 'The Principles of Art'

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12 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20420 The emotion expressed is non-conscious, but feels oppressive until expression relieves it [Collingwood]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
20421 Art exists ideally, purely as experiences in the mind of the perceiver [Collingwood, by Kemp]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
20406 Art clarifies the artist's mind and feelings, thus leading to self-knowledge [Collingwood, by Davies,S]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]