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

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Families,and the notation undergo radical alterations. Suppose, for instance, that . is a function from a set . to a set .. (The very choice of letters indicates that something strange is afoot.) An element of the domain . is called an ., . is called the ., the range of the function is called an ., the funct

流浪

严重伤害

Numbers, all unordered pairs {.}, with . in . in ., and . ≠ .. It seems clear that all the sets in the collection . have a property in common, namely the property of consisting of two elements. It is tempting to try to define “twoness” as the common property of all the sets in the collection ., but the temp

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天文台

Order,order plays an important role. The basic definitions are simple. The only thing to remember is that the primary motivation comes from the familiar properties of “less than or equal to” and not “less than.” There is no profound reason for this; it just happens that the generalization of “less than or

achlorhydria

,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.

hypotension

Well Ordering,artially ordered set is called . (and its ordering is called a .) if every non-empty subset of it has a smallest element. One consequence of this definition, worth noting even before we look at any examples and counterexamples, is that every well ordered set is totally ordered. Indeed, if . and . ar

ADAGE

Isolate

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.?