display all the ideas for this combination of texts
5 ideas
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
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From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |