generalization

Using particular facts or examples to work out a rule that applies more widely.

• Generalization from a few facts can be risky.
• Scientists use generalization to develop rules from repeated observations.
• Her reasoning involved generalization from individual cases.

How to use it: generalization from something to something (Generalization from these observations to a universal rule requires care.)

Similar words: induction, inductive reasoning

Opposites: deduction

Common phrases: inductive generalization, generalization from evidence, process of generalization

Forming a broad idea by finding features shared by several particular things.

• Generalization helps us group similar things.
• Through generalization, children learn that very different chairs belong to one category.
• The lesson encourages generalization from several examples.

How to use it: generalization from something (Generalization from familiar objects helps children form new categories.)

Similar words: abstraction

Common phrases: conceptual generalization, process of generalization, generalization from examples

A mathematical rule, idea, or problem that covers all cases of an earlier one and additional cases.

• The new theorem is a generalization of the old one.
• We need a generalization that works in four dimensions.
• Several generalizations of this formula appear in the textbook.

How to use it: a generalization of something (This formula is a generalization of the earlier equation.)

Similar words: extension

Opposites: specialization

Common phrases: generalization of something, natural generalization, mathematical generalization