Suppose students in two classes are shown to have sat an examination. Does that prove every student in the school sat it?
Yes if these are the only two classes and the claim is established for every student in both. No if a third class exists and has not been considered.
Complete induction therefore needs two checks:
1. Does the division cover the entire class?
2. Is the property established for every member of each part?
Opening interactive controls...
Induction: Complete and Incomplete Enumeration, Certainty and Probability
Suppose students in two classes are shown to have sat an examination. Does that prove every student in the school sat it?
Yes if these are the only two classes and the claim is established for every student in both. No if a third class exists and has not been considered.
Complete induction therefore needs two checks:
1. Does the division cover the entire class?
2. Is the property established for every member of each part?