Can you explain the differences or relationships between Darboux theorem and Riemann Integral? I thought that Darboux theorem was about derivative but why internet connects this with integral? It does not have to be so profound.. Please help me. Again I'm just a high school student so can you write more easier to understand?
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3Where does the Internet connect those two concepts? – José Carlos Santos Aug 16 '20 at 17:23
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I'm not sure but sometimes it does. Is there another theorem of Darboux that can confuse people like me? – TCLee Aug 16 '20 at 17:25
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1It is the definition of definite integral by Darboux, that can be proved to be equivalent to Riemann integral: https://en.wikipedia.org/wiki/Darboux_integral – Vincenzo Tibullo Aug 16 '20 at 17:25
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Oh now I understand.. So you mean that those are totally different theorem? – TCLee Aug 16 '20 at 17:27
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1One of them is a theorem. The other one is a definition. – José Carlos Santos Aug 16 '20 at 17:28
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OK. Thank you.^.^ – TCLee Aug 16 '20 at 17:30