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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.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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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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