Hairstyle For Women With Short Hair Why does differentiability imply continuity but continuity does not mean differentiability I am more interested in the part about a continuous function not being differentiable All I could find
begingroup Hibou57 I have seen the symbol implies used to mean different things I was taking it to be the logical connective of material implication which some people instead call If we change f is continuous on a b to f is Riemann integrable does the mean value theorem for integral still holds If not Can you give me a counter example I know that
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Typically one uses rightarrow to mean imply only in the context of writing out formal sentences in a propositional calculus i e forall a exists b p a rightarrow q b A materially implies B does not mean A therefore B In a propositional logic formula names city names state names cannot be substituted for letters A B C etc
If X then Y that is X implies Y You want to know if the implication is true Call X the assumption and Y the conclusion If your assumptions are false then it does not matter if Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow the largest most trusted online community for
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We also know that P implies Q is false when P is true and Q is false Now one answer that I have seen on this site says that P does not imply Q means lnot P to Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow the largest most trusted online community for developers to learn share their
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Why does differentiability imply continuity but continuity does not mean differentiability I am more interested in the part about a continuous function not being differentiable All I could find 

https://math.stackexchange.com › questions
 begingroup Hibou57 I have seen the symbol implies used to mean different things I was taking it to be the logical connective of material implication which some people instead call 

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