Principle of Mathematical Induction (weak PMI) (If the statement is true at the starting index n0, and truth for n)
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If the statement is true at the starting index n0, and truth for n equals k implies truth for k plus one, then it holds for every integer n at least n0.
What each symbol means
| Symbol | What it stands for |
|---|---|
| k | Generic integer in the inductive step |
| n_0 | Base case starting integer (often 1) |
| P(n) | Proposition (open sentence) indexed by n |
When to use this
P must be well-defined on integers n ≥ n0; inductive step must use the induction hypothesis P(k) legitimately.