Postulate
High school
A postulate is a statement accepted without proof as a starting point, especially in geometry, as in Euclid’s postulates.
Examples
Examples
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Euclid’s parallel postulate
High school
Euclid’s parallel postulate is a postulate, and so an axiom, because Euclidean geometry takes it as given without proof.
Non-examples
Things that may be mistaken for examples.
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The statement “$f$ is continuous on $[a, b]$,” in the intermediate value theorem
Undergraduate
The assumption “$f$ is continuous on $[a, b]$” is not a postulate, because it is a condition on $f$, not a foundation of a theory.
Properties
- In modern mathematics, “postulate” and axiom are synonyms. Euclid used “postulate” for geometric assumptions and “common notion” for general ones, such as “things equal to the same thing are equal to each other.”