Titlebook: Naive Set Theory; Paul R. Halmos Book 1974 Springer Science+Business Media New York 1974 addition.arithmetic.Cardinal number.Countable set

Observe

The Axiom of Specification,t of these basic principles of set manufacture says, roughly speaking, that anything intelligent one can assert about the elements of a set specifies a subset, namely, the subset of those elements about which the assertion is true.

Urgency

Inverses and Composites,ch subset A of . the image subset .(.) of .. The algebraic behavior of the mapping . → .(.) leaves something to be desired. It is true that if {..} is a family of subsets of ., then.(proof?), but the corresponding equation for intersections is false in general (example?), and the connection between images and complements is equally unsatisfactory.

CARE

,Zorn’s Lemma,ormulated (or, if need be, reformulated) so that the underlying set is a partially ordered set and the crucial property is maximality. Our next purpose is to state and prove the most important theorem of this kind.

aqueduct

Transfinite Recursion,way of getting the value of the function at each non-zero element . of . from its value at the element preceding .. The transfinite analogue constructs a function on any well ordered set .; the raw material is a way of getting the value of the function at each element . of . from its values at all the predecessors of ..

無(wú)政府主義者

Ordinal Numbers,ntains .. What happens if we start with ., form its successor .., then form the successor of that, and proceed so on ad infinitum? In other words: is there something out beyond ., .., (..)., ?, etc., in the same sense in which . is beyond 0, 1, 2, ?, etc.?

不可知論

978-0-387-90104-6Springer Science+Business Media New York 1974

POWER

Naive Set Theory978-1-4757-1645-0Series ISSN 0172-6056 Series E-ISSN 2197-5604

Tincture

Unordered Pairs,For all that has been said so far, we might have been operating in a vacuum.

可行

Complements and Powers,If . and . are sets, the . between . and ., more often known as the . of . in ., is the set . defined by

外向者

Ordered Pairs,What does it mean to arrange the elements of a set . in some order?