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Definition: Power Set

Let $X$ be a set. The axiom of power set and the axiom of empty ensure * the existence of the power set, $\mathcal P(X) :=\{A\mid A\subseteq X\}$, i.e. the set of all possible subsets of $X$¹, and
* that the empty set $\emptyset$ is a subset any non-empty set $X$.

Mentioned in:

Applications: 1
Axioms: 2
Corollaries: 3
Definitions: 4 5 6
Examples: 7 8
Explanations: 9
Parts: 10
Proofs: 11 12 13 14
Propositions: 15 16

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References

Bibliography

1. Reinhardt F., Soeder H.: "dtv-Atlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition

Footnotes