(d) Therefore n = s(0), because ... (e) Therefore n = 1, because ...

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 30EQ
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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...
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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