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Define a set S recursively as follows: I. BASE: 0 € S II. RECURSION: If sЄ S, then a. s+3 ES b. s-3 € S III. RESTRICTION: Nothing is in S other than objects defined in I and II above. Use structural induction to prove that every integer in S is divisible by 3.

Define a set S recursively as follows: I. BASE: 0 € S II. RECURSION: If sЄ S, then a. s+3 ES b. s-3 € S III. RESTRICTION: Nothing is in S other than objects defined in I and II above. Use structural induction to prove that every integer in S is divisible by 3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Define a set S recursively as follows: I. BASE: 0 € S II. RECURSION: If sЄ S, then a. s+3 ES b. s-3 € S III. RESTRICTION: Nothing is in S other than objects defined in I and II above. Use structural induction to prove that every integer in S is divisible by 3.
Transcribed Image Text:Define a set S recursively as follows: I. BASE: 0 € S II. RECURSION: If sЄ S, then a. s+3 ES b. s-3 € S III. RESTRICTION: Nothing is in S other than objects defined in I and II above. Use structural induction to prove that every integer in S is divisible by 3.
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