Answered: Show that the set of all real numbers…

Show that the set of all real numbers of the form a0 + a1π + a2π2 + · · · + anπn with ai ∈ Z and n ∈ N is a subring of R that contains both Z and π

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.1: Definition Of A Ring

Problem 18E: 18. Find subrings and of such that is not a subring of .

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Question

Show that the set of all real numbers of the form
a₀ + a₁π + a₂π² + · · · + a_nπⁿ
with a_i ∈ Z and n ∈ N is a subring of R that contains both Z and π

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