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🚧 Middle of 5.2

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appendix_b.txt
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chapter_5/exercises.md
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chapter_5/test_yourself.md
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1. Mathematical induction is a method for proving that a property defined for 1. Mathematical induction is a method for proving that a property defined for
integers $n$ is true for all values of $n$ that are _____. integers $n$ is true for all values of $n$ that are _____.
greater than or equal to some initial value.
2. Let $P(n)$ be a property defined for integers $n$ and consider constructing a 2. Let $P(n)$ be a property defined for integers $n$ and consider constructing a
proof by mathematical induction for the statement "P(n) is true for all proof by mathematical induction for the statement "P(n) is true for all
$n \geq a$." $n \geq a$."
a. In the basis step one must show _____. a. In the basis step one must show _____.
that $P(a)$ is true.
b. In the inductive step one supposes that _____ for a particular but b. In the inductive step one supposes that _____ for a particular but
arbitrarily chosen value of an integer $k \geq a$. This supposition is called arbitrarily chosen value of an integer $k \geq a$. This supposition is called
the _____. One then has to show that _____. the _____. One then has to show that _____.
$P(k)$ is true; inductive hypothesis; $P(k + 1)$ is true.

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