(d) Therefore n = s(0), because ... (e) Therefore n = 1, because ...
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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I only need help from d to e
![1. Suppose we want to argue, by using the definitions and axioms from our lecture on
Peano arithmetic, that if n + 1 = 2 for some n € No, then n = 1. Give a justification for
each of steps in the proof: each justification is either an axiom or a definition.
We start by assuming that n + 1 = 2, where n € No.
(a) Therefore n + s(0) = s(s(0)), because ...
(b) Therefore s(n+0) = s(s(0)), because...
(c) Therefore s(n) = s(s(0)), because...
(d) Therefore n = s(0), because ...
(e) Therefore n = 1, because...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F232028c3-8426-43ce-b04a-a507a5240356%2F602a1d8d-bfed-476d-98fd-9450f357b439%2Fxtpopz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose we want to argue, by using the definitions and axioms from our lecture on
Peano arithmetic, that if n + 1 = 2 for some n € No, then n = 1. Give a justification for
each of steps in the proof: each justification is either an axiom or a definition.
We start by assuming that n + 1 = 2, where n € No.
(a) Therefore n + s(0) = s(s(0)), because ...
(b) Therefore s(n+0) = s(s(0)), because...
(c) Therefore s(n) = s(s(0)), because...
(d) Therefore n = s(0), because ...
(e) Therefore n = 1, because...
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