CS336f108 - 9/19/10 1 Lecture 8 CS336 f10 Inductively...

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Unformatted text preview: 9/19/10 1 Lecture 8 CS336 f10 Inductively Defined Sets What Well Discuss Inductively defined sets Inductively defined functions Proofs by Mathematical Induction Specifying sets by Induction Sets can be specified by: enumeration (useful only for small sets) a defining property a predicate that filters out some elements of some previously defined (larger) set. A third and important method is inductive construction. Inductive definitions of sets have three clauses. Letting S be the set being defined, these are Basis: a0,a1,,an S. Establishes that S , and characterizes a finite set of atoms from which the sets other elements are constructed. Inductive definitions of sets have three clauses. Letting S be the set being defined, these are Basis: a0,a1,,an S. Establishes that S , and characterizes a finite set of atoms from which the sets other elements are constructed. Induction: if x0,,xm S then f(x0,,xm) S. The function f specifies how to combine elements of S to form new elements of S; it is known as the sets constructor. Inductive definitions of sets have three clauses....
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CS336f108 - 9/19/10 1 Lecture 8 CS336 f10 Inductively...

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