Our (high-school) workbook had a statement that confuses me, since I always viewed the expression $x!$ to be defined for integers only. How is the factorial function defined for decimal numbers ?
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4The extension to the real and complex number is the Gamma function. https://en.wikipedia.org/wiki/Gamma_function – CyclotomicField Sep 24 '23 at 16:47
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3Who says it's continuous for all values greater than $2$? I agree with your assessment: at least from a high school perspective, it cannot be considered continuous, as it is defined only on non-negative integer points. – Theo Bendit Sep 24 '23 at 16:51
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The textbook says it's continuous for x>2. – CarnotEngine Sep 24 '23 at 17:28
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Well then the textbook is wrong, or at least misleading. – cpiegore Sep 24 '23 at 18:06
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@cpiegore To be fair, one has to see the workbook. Perhaps there is a scan available? – Dietrich Burde Sep 24 '23 at 18:08
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Nope, it's a school-issued textbook, so I'm pretty sure you won't find a scan of it – CarnotEngine Sep 25 '23 at 04:21