The statement “$f$ is continuous on $[a, b]$,” in the intermediate value theorem

Example · Undergraduate

Terms

Term	This example	Why
assumption	✓	“$f$ is continuous on $[a, b]$” is an assumption of the intermediate value theorem, because the theorem is proved only for continuous $f$.
axiom	✗	The assumption “$f$ is continuous on $[a, b]$” is not an axiom, because it is a condition on $f$, not a foundation of a theory.
postulate	✗	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.

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