Lecture_12_09 - Lecture 12 Lecture 12 Inductively defined...

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Unformatted text preview: Lecture 12 Lecture 12 Inductively defined sets Inductively defined sets Top down Bottom up Examples: natural numbers, language of PL. Define the following using zero and the successor function: {(x,y) : x < y} {(x,y,z) : x,y,z, ∈ N and x+y = z} Proof by induction Proof by induction Statement and why it works. Examples: Show that the proposal for an inductive def. of{(x,y) : x < y} is correct. Show that the proposal for an inductive def. of {(x,y,z) : x,y,z, ∈ N and x+y = z} is correct. ...
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