Definition
Inductive reasoning
Inductive reasoning uses examples or patterns to suggest a general rule that still needs proof.
What it means
Look across several examples and ask what rule they seem to share. That is useful for making a conjecture. Then remember: more examples can strengthen the guess, but a proof must cover every allowed case.
Remember it
Examples point toward a rule; they do not lock the rule in place.
Example
The sums 1 + 3 = 4, 3 + 5 = 8, and 5 + 7 = 12 are all even. These cases suggest the conjecture “the sum of two odd numbers is even,” but the three examples alone do not prove it for all odd numbers.
Watch for
Inductive reasoning is not mathematical induction. Mathematical induction is a deductive proof method that establishes all cases in a sequence.
Common mix-up
Deduction proves what must follow from facts. Inductive reasoning proposes what may be generally true after seeing examples.
Exact meaning
Inductive reasoning forms a general conjecture from observed examples, cases, or patterns. It can make a claim plausible, but checking examples alone does not prove that the claim holds in every case.