Philosophy Lexicon of Arguments

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Empty set: an empty set is a set without an element. Notation ∅ or {}. There is only one empty set, since without an existing element there is no way to specify a specification of the set. The empty set can be specified as such that each element of the empty set is not identical with itself {x x unequal x}. Since there is no such object, the set must be empty. The empty set is not the number zero, but zero indicates the cardinality of the empty set.

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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.
 
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16
empty set / Stechow: is a subset, but not element of any set. - Proof: Let M be an arbitrary set and x is any one thing. We show that the following applies: if x e 0, then x e M. ( "A then B" is equivalent to Not A or B): This is true iff. x ~e 0 or x e M. Now, for every x: x ~ e 0. So the statement that the empty set is subset of any set is valid.


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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.
A. von Stechow
I Arnim von Stechow Schritte zur Satzsemantik
www.sfs.uniï·"tuebingen.de/~astechow/Aufsaetze/Schritte.pdf (26.06.2006)




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Ed. Martin Schulz, access date 2017-06-27