Transfinite Induction
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Transfinite induction is an extension of mathematical induction to well-ordered sets, for instance to sets of ordinals or cardinals. Let P( ) be a property defined for all ordinals . Suppose that whenever P( ) is true for all , then P( ) is also true. Then transfinite induction tells us that P is true for all ordinals. That is, if P( ) is true whenever P( ) is true for all , then P( ) is true for all . Or, more practically: in order to prove a property P for all…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Transfinite induction is an extension of mathematical induction to well-ordered sets, for instance to sets of ordinals or cardinals. Let P( ) be a property defined for all ordinals . Suppose that whenever P( ) is true for all , then P( ) is also true. Then transfinite induction tells us that P is true for all ordinals. That is, if P( ) is true whenever P( ) is true for all , then P( ) is true for all . Or, more practically: in order to prove a property P for all ordinals , one can assume that it is already known for all smaller .