Concept
Empty set
Overview
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.
Any set other than the empty set is called non-empty.
In some textbooks and popularizations, the empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty).
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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367. Indeed, confusion springs, more often than not, from ambiguity in terms, and from one's failure to take trouble over gaining clear ideas about them. That gives rise to these eternal, and usually mistaken, contentions on necessity and contingency, on the possible and the impossible. But provided that it is understood that necessity and possibility, taken metaphysically and strictly, depend solely upon this…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
States what Empty set is; the author is tied to Empty set in the knowledge graph.
This property of quantities, according to which no part of them is the smallest possible (no part simple), is called their continuity. Space and time are quanta continua, because no part of them can be given, without enclosing it within boundaries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only…
Immanuel Kant, The Critique of Pure Reason
States what Empty set is.
This improvement also is due to Cantor, and it is one which has revolutionised mathematics. Only order is now relevant to limits. Thus, for instance, the smallest of the infinite integers is the limit of the finite integers, though all finite integers are at an infinite distance from it. The study of different types of series is a general subject of which the study of ordinal numbers (mentioned above) is a special…
Bertrand Russell, Mysticism and Logic and Other Essays
States what Empty set is.
Philosophers who discussed Empty set
Related ideas
- First-order logic
- Finite set
- Harvard University Press
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- Ontology
- Intersection (set theory)
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- Peano axioms
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- E. J. Lowe (philosopher)
- Zermelo set theory
- George Boolos
- 0
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Opposing perspectives
Place in the tradition
Part of Description logic.