Mintys.MatematikosIšsiaiškinimoBūdai istorijaPaslėpti nežymius pakeitimus  Rodyti galutinio teksto pakeitimus 2016 birželio 18 d., 17:38
atliko 
Pakeistos 146 eilutės iš
ZermeloFraenkel axioms of set theory * Axiom of Extensionality. Two sets are the same set if they have the same elements. * Axiom of Regularity. Every nonempty set x contains a member y such that x and y are disjoint sets. This implies, for example, that no set is an element of itself and that every set has an ordinal rank. * Axiom Schema of Specification. The subset of a set z obeying a formula ϕ(x) with one free variable x always exists. * Axiom of Pairing. If x and y are sets, then there exists a set which contains x and y as elements. * Axiom of Union. The union over the elements of a set exists. * Axiom Schema of Replacement. The image of a set under any definable function will also fall inside a set. * Axiom of Power Set. For any set x, there is a set y that contains every subset of x. * WellOrdering Theorem. For any set X, there is a binary relation R which wellorders X. Also: * Axiom of infinity. Let S(w) abbreviate w ∪ {w}, where w is some set. Then there exists a set X such that the empty set ∅ is a member of X and, whenever a set y is a member of X, then S(y) is also a member of X. Implicit math: Sets are simplexes. Are simplexes defined by their subsimplexes as well? * Wellordering theorem. Each vertex is related by edges to the other vertices. Established by the qweight. * Axiom of power set. The power sets are the lattice paths in Pascal's triangle. * Axiom of union. Simplexes combine to form larger simplexes. * Axiom of pairing. Simplexes can be "collapsed" or "represented" by a vertex, the highest vertex. Two vertices are linked by an edge. * Axiom of regularity. * Axiom of extensionality. Simplexes are defined by their vertices. And the edges? Eightfold way * Axiom of Pairing. If x and y are sets, then there exists a set which contains x and y as elements. * Axiom of Extensionality. Two sets are the same set if they have the same elements. * Axiom of Union. The union over the elements of a set exists. * Axiom of Power set. For any set x, there is a set y that contains every subset of x. * Axiom of Regularity. Every nonempty set x contains a member y such that x and y are disjoint sets. * Wellordering theorem. For any set X, there is a binary relation R which wellorders X. * Axiom Schema of Specification. The subset of a set z obeying a formula ϕ(x) with one free variable x always exists. * Axiom Schema of Replacement. The image of a set under any definable function will also fall inside a set. Reorganizings * Evolution. Tree of variations. Axiom of Pairing (subbranches are part of a branch). * Atlas. Adjacency graph. Axiom of Extensionality. Two levels of equality. * Handbook. Total order. WellOrdering Theorem. * Chronicle. Powerset lattice. Axiom of Power Set. * Catalog. Decomposition. Axiom of Union. * Tour. Directed graph. Axiom of Regularity. Relate to multiplication http: į:
Žr. [[Book/MathDiscovery]] 2016 birželio 18 d., 01:20
atliko 
Pakeistos 3741 eilutės iš
* Evolution. Tree of variations. * Handbook. Total order. * Chronicle. Powerset lattice į:
* Evolution. Tree of variations. Axiom of Pairing (subbranches are part of a branch). * Atlas. Adjacency graph. Axiom of Extensionality. Two levels of equality. * Handbook. Total order. WellOrdering Theorem. * Chronicle. Powerset lattice. Axiom of Power Set. * Catalog. Decomposition. Axiom of Union. 2016 birželio 18 d., 01:16
atliko 
Pakeistos 4246 eilutės iš
* Tour. Directed graph. Axiom of Regularity. į:
* Tour. Directed graph. Axiom of Regularity. Relate to multiplication http://www.selflearners.net/uploads/multiplicationmodels.png 2016 birželio 18 d., 01:11
atliko 
Pakeistos 3742 eilutės iš
* Evolution. * * į:
* Evolution. Tree of variations. * Atlas. Adjacency graph. * Handbook. Total order. * Chronicle. Powerset lattice. WellOrdering Theorem. * Catalog. Decomposition. * Tour. Directed graph. Axiom of Regularity. 2016 birželio 18 d., 01:10
atliko 
Pridėtos 3542 eilutės:
Reorganizings * Evolution. * Atlas. * Handbook. * Chronicle. Total order. * Catalog. * Tour. Directed graph. 2016 birželio 18 d., 00:58
atliko 
Pakeistos 713 eilutės iš
* Axiom * Axiom of * Axiom of * Axiom * Axiom of į:
* Axiom Schema of Specification. The subset of a set z obeying a formula ϕ(x) with one free variable x always exists. * Axiom of Pairing. If x and y are sets, then there exists a set which contains x and y as elements. * Axiom of Union. The union over the elements of a set exists. * Axiom Schema of Replacement. The image of a set under any definable function will also fall inside a set. * Axiom of Power Set. For any set x, there is a set y that contains every subset of x. * WellOrdering Theorem. For any set X, there is a binary relation R which wellorders X. Pakeista 17 eilutė iš:
Implicit math: Sets are simplexes. į:
Implicit math: Sets are simplexes. Are simplexes defined by their subsimplexes as well? Pakeistos 2134 eilutės iš
* Axiom of pairing. į:
* Axiom of pairing. Simplexes can be "collapsed" or "represented" by a vertex, the highest vertex. Two vertices are linked by an edge. * Axiom of regularity. * Axiom of extensionality. Simplexes are defined by their vertices. And the edges? Eightfold way * Axiom of Pairing. If x and y are sets, then there exists a set which contains x and y as elements. * Axiom of Extensionality. Two sets are the same set if they have the same elements. * Axiom of Union. The union over the elements of a set exists. * Axiom of Power set. For any set x, there is a set y that contains every subset of x. * Axiom of Regularity. Every nonempty set x contains a member y such that x and y are disjoint sets. * Wellordering theorem. For any set X, there is a binary relation R which wellorders X. * Axiom Schema of Specification. The subset of a set z obeying a formula ϕ(x) with one free variable x always exists. * Axiom Schema of Replacement. The image of a set under any definable function will also fall inside a set. 2016 birželio 18 d., 00:46
atliko 
Pakeistos 1112 eilutės iš
* Axiom of power set. For any set x, there is a set y that contains every subset of x į:
* Axiom of power set. For any set x, there is a set y that contains every subset of x * Wellordering theorem. For any set X, there is a binary relation R which wellorders X. Also: * Axiom of infinity. Let S(w) abbreviate w ∪ {w}, where w is some set. Then there exists a set X such that the empty set ∅ is a member of X and, whenever a set y is a member of X, then S(y) is also a member of X. Implicit math: Sets are simplexes. * Wellordering theorem. Each vertex is related by edges to the other vertices. Established by the qweight. * Axiom of power set. The power sets are the lattice paths in Pascal's triangle. * Axiom of union. Simplexes combine to form larger simplexes. * Axiom of pairing. 2016 birželio 18 d., 00:28
atliko 
Pridėtos 112 eilutės:
Attach:matematikosissiaiskinimobudai.png ZermeloFraenkel axioms of set theory * Axiom of Extensionality. Two sets are the same set if they have the same elements. * Axiom of Regularity. Every nonempty set x contains a member y such that x and y are disjoint sets. This implies, for example, that no set is an element of itself and that every set has an ordinal rank. * Axiom schema of specification. The subset of a set z obeying a formula ϕ(x) with one free variable x always exists. * Axiom of pairing. If x and y are sets, then there exists a set which contains x and y as elements. * Axiom of union. The union over the elements of a set exists. * Axiom schema of replacement. The image of a set under any definable function will also fall inside a set. * Axiom of power set. For any set x, there is a set y that contains every subset of x. * Axiom of infinity. Let S(w) abbreviate w ∪ {w}, where w is some set. Then there exists a set X such that the empty set ∅ is a member of X and, whenever a set y is a member of X, then S(y) is also a member of X. 
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