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Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y = S, then: • x+y=S • x-yes Prove that every element in S is divisible by 7.

Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y = S, then: • x+y=S • x-yes Prove that every element in S is divisible by 7.

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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Complete the basis step of the proof. What is the inductive hypothesis? What do you need to show in the inductive step of the proof? Complete the inductive step of the proof.
Transcribed Image Text:Complete the basis step of the proof. What is the inductive hypothesis? What do you need to show in the inductive step of the proof? Complete the inductive step of the proof.
Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y = S, then: • x+y=S • x-yes Prove that every element in S is divisible by 7.
Transcribed Image Text:Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y = S, then: • x+y=S • x-yes Prove that every element in S is divisible by 7.
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