| 1. | That fact can also be proven by using the intermediate value theorem.
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| 2. | Hence, the intermediate value theorem ensures that the equation has a solution.
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| 3. | The intermediate value theorem says that every continuous function is a Darboux function.
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| 4. | Thus f satisfies a property stronger than the conclusion of the intermediate value theorem.
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| 5. | Thus f is a spectacular counterexample to the converse of the intermediate value theorem.
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| 6. | From the intermediate value theorem, has at least roots.
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| 7. | In this case, the Brouwer fixed-point theorem follows almost immediately from the intermediate value theorem.
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| 8. | Using this definition, he proved the Intermediate Value Theorem.
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| 9. | The main mathematical tool used by Austin's procedure is the intermediate value theorem ( IVT ).
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| 10. | Another proof can be given by combining the mean value theorem and the intermediate value theorem.
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