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Exercise 14 - Chapter 3

edited June 2018 in Exercises

In Example 3.12 we identified the paths of the loop graph (3.13) with numbers \( n \in \mathbb{N} \) . Paths can be concatenated. Given numbers \( m, n \in \mathbb{N} \) , what number corresponds to the concatenation of their associated paths?

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  • 1.
    edited July 2018

    \(m+n\). Since \(n=s^n(0)\) and \(m=s^m(0)\), concatenation gives \(s^{n}(s^m(0))=s^{(n+m)}(0)=n+m\). So, concatenation corresponds to summation, and is commutative (since there is only one symbol/function being concatenated).

    Comment Source:\\(m+n\\). Since \\(n=s^n(0)\\) and \\(m=s^m(0)\\), concatenation gives \\(s^{n}(s^m(0))=s^{(n+m)}(0)=n+m\\). So, concatenation corresponds to summation, and is commutative (since there is only one symbol/function being concatenated).
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