Case A: A class contains exactly eight students. Each one is checked and found present. “Every student in this class is present” is complete induction.
Case B: Eight classes in a city have full attendance. “Every class in the city has full attendance” is incomplete, because other classes were not examined.
The word “all” does not settle the issue. We must identify which entire set is under discussion and determine whether it was fully investigated.
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Induction: Complete and Incomplete Enumeration, Certainty and Probability
Case A: A class contains exactly eight students. Each one is checked and found present. “Every student in this class is present” is complete induction.
Case B: Eight classes in a city have full attendance. “Every class in the city has full attendance” is incomplete, because other classes were not examined.
The word “all” does not settle the issue. We must identify which entire set is under discussion and determine whether it was fully investigated.