In mathematics, <math>\in</math>-induction (epsilon-induction) is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P[x]. If the truth of the property for x follows from its truth for all elements of x, for every set x, then the property is true of all sets.

PropertyValue
dbpprop:abstract
  • In mathematics, <math>\in</math>-induction (epsilon-induction) is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P[x]. If the truth of the property for x follows from its truth for all elements of x, for every set x, then the property is true of all sets. In symbols: <math>\forall x (\forall y \rightarrow P) \rightarrow \forall x P[x]</math> This principle, sometimes called the axiom of induction (in set theory), is equivalent to the axiom of regularity. <math>\in</math>-induction is a special case of well-founded induction. The name is most often pronounced "epsilon-induction", because the set membership symbol <math>\in</math> historically developed from the Greek letter <math>\epsilon </math>.
dbpprop:hasPhotoCollection
rdfs:comment
  • In mathematics, <math>\in</math>-induction (epsilon-induction) is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P[x]. If the truth of the property for x follows from its truth for all elements of x, for every set x, then the property is true of all sets.
rdfs:label
  • Epsilon-induction
owl:sameAs
skos:subject
foaf:page
is dbpprop:disambiguates of
is dbpprop:redirect of