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 Well-order If a set is well-ordered, the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the
Наименование:

Well-order

автор Lambert M. S. издательство Книга по Требованию Математический анализ. Кратные и криволинейные интегралы. Задачи, решения
Cтраниц 68        мягкая обложка       
Аннотация:If a set is well-ordered, the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the set. The well-ordering theorem is also equivalent to the Kuratowski-Zorn lemma. The well-ordering theorem, which is equivalent to the axiom of choice, states that every set can be well-ordered. The observation that the natural numbers are well-ordered by the usual less-than relation is commonly called the well-ordering principle. Equivalently, a well-ordering is a well-founded total order. Every element s, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound. The set S together with the well-order relation is then called a well-ordered set. There may be elements (besides the least element) which have no predecessor. In mathematics, a well-order relation (or well-ordering) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.
Автор: Lambert M. S.
Издательство: Книга по Требованию
Год:2010
Цена:
1190 руб
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Поиск: Well-order


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Special fields of psychology

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