Inductive reasoning is a form of logic that looks for a pattern, and then applies it as a rule.

For example, given the sequence 2, 4, 6, 8, ______, what might belong in the blank? If you said 10, then you used inductive reasoning, by noticing a pattern that each term in the series increases by 2 from the previous term.

Examples of statements that use inductive reasoning:

- All ice I have ever observed is cold, therefore all ice is cold.
- I have always gotten an A in math class, therefore I will get an A in this math class.
- All odd numbers are prime.

Problems with Inductive Reasoning

While it is a possible that statements that use inductive reasoning are true, it is difficult to prove the statements true. For example, in the first statement above about ice, how do we know we have observed all possible kinds of ice? Maybe there exists a form of ice that isn't cold. It is easier to see why the middle statement uses faulty reasoning, as past experiences in math class do not necessarily predict future math classes. The last statement about odd numbers is false, and this helps us see what is useful about inductive reasoning.

Usefulness of Inductive Reasoning

Inductive reasoning can be used to prove a statement is false by using counterexamples. For example, the statement "All odd numbers are prime" can be disproved by producing at least one instance where this is not true, such as the number 9.

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