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## Homework Statement

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.

## Homework Equations

## The Attempt at a Solution

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

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