Observe
发表于 2025-3-28 15:36:40
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
发表于 2025-3-28 20:48:18
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
发表于 2025-3-28 23:15:03
,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
发表于 2025-3-29 07:00:45
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 ..
无政府主义者
发表于 2025-3-29 08:13:47
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.?
不可知论
发表于 2025-3-29 12:25:02
978-0-387-90104-6Springer Science+Business Media New York 1974
POWER
发表于 2025-3-29 19:12:44
Naive Set Theory978-1-4757-1645-0Series ISSN 0172-6056 Series E-ISSN 2197-5604
Tincture
发表于 2025-3-29 23:48:56
Unordered Pairs,For all that has been said so far, we might have been operating in a vacuum.
可行
发表于 2025-3-30 00:39:45
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
发表于 2025-3-30 07:47:46
Ordered Pairs,What does it mean to arrange the elements of a set . in some order?