Principle of Strong (Complete) Mathematical Induction (If P holds at the start, and whenever P is true for every integer from)
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If P holds at the start, and whenever P is true for every integer from n0 through k it follows that P(k+1) is true, then P holds for all integers from n0 onward.
What each symbol means
| Symbol | What it stands for |
|---|---|
| k | Integer at which all earlier cases are assumed |
| n_0 | Starting index (may need several consecutive bases) |
| P(n) | Proposition indexed by n |
When to use this
Inductive step must use whichever of P(n0), …, P(k) are actually needed; multi-base versions are common when P(k+1) refers to smaller indices.