What does the textbook mean by Hypothesis here

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I am reading through page 278 of the textbook "Calculus: Early Transcendentals" 8th Edition, by James Stewart. I am confused by his use of the word "hypothesis" here. I thought a hypothesis was essentially an educated guess?

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What does the author mean by "hypothesis" here?

Best Answer

Well you must have read the Extreme Value Theorem. It has "assumption" and "results". The "assumptions" are called hypotheses:

Extreme Value Theorem:

Hypothesis: Let $f$ be a continuous, real-valued function to the closed interval $[a,b]$

Conclusion: Then $f$ attains extreme values on that interval

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