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3.42. Let G be the set of all sequences of integers (a₁, a2, a3, . . .). 1. Show that G is a group under (a₁, a2, ...) + (b₁, b₂, ...) = (a₁ + b₁, a₂ + b₂,...). 2. Let H be the set of all elements (a₁, a2, ...) of G such that only finitely many a are different from 0 (and (0, 0, 0, ...) E H). Show that H is a subgroup of G.

3.42. Let G be the set of all sequences of integers (a₁, a2, a3, . . .). 1. Show that G is a group under (a₁, a2, ...) + (b₁, b₂, ...) = (a₁ + b₁, a₂ + b₂,...). 2. Let H be the set of all elements (a₁, a2, ...) of G such that only finitely many a are different from 0 (and (0, 0, 0, ...) E H). Show that H is a subgroup of G.

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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3.42. Let G be the set of all sequences of integers (a₁, a2, a3, . . .). 1. Show that G is a group under (a₁, a2, ...) + (b₁, b₂, ...) = (a₁ + b₁, a₂ + b₂,...). 2. Let H be the set of all elements (a₁, a2, ...) of G such that only finitely many a are different from 0 (and (0, 0, 0, ...) E H). Show that H is a subgroup of G.
Transcribed Image Text:3.42. Let G be the set of all sequences of integers (a₁, a2, a3, . . .). 1. Show that G is a group under (a₁, a2, ...) + (b₁, b₂, ...) = (a₁ + b₁, a₂ + b₂,...). 2. Let H be the set of all elements (a₁, a2, ...) of G such that only finitely many a are different from 0 (and (0, 0, 0, ...) E H). Show that H is a subgroup of G.
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