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#flo #disorganized #incomplete
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\[ \mathbf{R} \text{ vs } \mathbb{R} \]
1 Proof by Induction
Using Axler 2.C 10 as an example.
1.1 Induction building blocks
1.1.1 Base Case:
Prove for the simplest case
Prove for \(\mathcal{P}_0(\mathbb{R})\).
1.1.2 Inductive Step
Show that if case \(n\) is correct, then case \(n+1\) is also correct
Assume that it works for \(\mathcal{P}_i(\mathbb{R})\), then prove it for \(\mathcal{P}_{i+1}(\mathbb{R})\).