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Reversed limit definition for monotonic functions
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[QUOTE="fresh_42, post: 5811390, member: 572553"] You can define whatever you like, as long as it is well defined. For this reason it should be helpful to indicate which variable depends on which and to explicitly write the quantors. If I read it correctly, then ##\varepsilon = \varepsilon(\delta)##. But then I have difficulties with the next line. I read ##\forall \, \delta \, \exists \, \varepsilon(\delta)\, : \,\vert \, f(x)-L\,\vert \, < \varepsilon(\delta) \Longrightarrow \,\vert \,x-a\,\vert \,< \delta \,##. The order of the quantors don't seem to reflect to the order of the conclusion. And how do you specify ##L##\,? The remaining question is in any case: What for? [/QUOTE]
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Reversed limit definition for monotonic functions
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