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Reversed limit definition for monotonic functions
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[QUOTE="ecoo, post: 5811271, member: 502550"] [h2]Homework Statement [/h2] Does the delta-epsilon limit definition in reverse work for describing limits in monotonic functions? By reversed, one means for lim (x -> a) f(x) = L if for each δ there corresponds ε such that 0 < | x-a | < δ whenever | f(x) - L | < ε. [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] I am thinking that it works, because this definition means that the range interval must lie within the domain interval, and it can be seen that shrinking δ also shrinks ε, which is how the usual definition works but in reverse. I don't think this would work for non-monotonic functions because there can be many f(x) that satisfy | f(x) - L | < ε but not | f(x) - L | < ε. Hopefully someone can also confirm this part too. Thanks [/QUOTE]
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Reversed limit definition for monotonic functions
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