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CS336f108

# CS336f108 - Lecture 8 CS336 f10 What Well Discuss...

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9/19/10 1 Lecture 8 CS336 f10 Inductively Defined Sets What We’ll 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 set’s 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 set’s 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 set’s constructor.

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CS336f108 - Lecture 8 CS336 f10 What Well Discuss...

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