Continuity Vs IVT

Question

Just wondering whether we can define continuity by Intermediate Value Theorem classically? I mean, are they both equivalent i.e. a function f is continues iff f satisfy IVT? Cheers!

There are functions which have intermediate value property but are discontinuous. See this. — edm, Jul 16 '17 at 23:57
However: You might try to prove this as an exercise. If $f$ takes on each value only finitely many times and has the IVP, then $f$ must be continuous. — Ted Shifrin, Jul 17 '17 at 00:17

score 3 · Accepted Answer · answered Jul 17 '17 at 00:04

3

There are nowhere -continuous functions with the IVT property, e.g.: https://en.wikipedia.org/wiki/Conway_base_13_function

answered Jul 17 '17 at 00:04

gary

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Continuity Vs IVT

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