|Ordinal numbers: ordinals indicate the position of elements within a sequence (expressed by "first", "second", ...). In contrast, cardinal numbers (expressed by "one," two ", ...) indicate the size (cardinality) of sets. See also numbers, sets, order, well-ordering._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
|Thiel I 199
Transfinite Ordinal Numbers/Cantor: we start from the basic numbers again, not only for counting, but now also with the aim of arranging. Now we also want to specify in which order the elements of a set are to be considered in a context.
Def Ordered: A set is called ordered by KL, if for each two different of its elements a and b either aKb or bKa is valid.
Arrangements are called w. There are very different arrangement possibilities.
Def Pairterm: Then the representation of the relation term representing the order relation is additionally required: the "Pairterm".
When comparing ordered sets, the term "illustration" is used._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Philosophie und Mathematik Darmstadt 1995