Suppose that f is continuous on [a,b] but not uniformly continuous on [a,b].
Then, there exists an ε>0 such that for every δ>0, there are x,y∈[a,b], depending on δ, such that
|x−y|<δ and |f(x)−f(y)|≥ε.
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718 |
| by EngliSea on 2020-07-17 | |
| ᐥLet f be defined and continuous on [a,b]. Then f is uniformly continuous on [a,b].ᐥ Suppose that f is continuous on [a,b] but not uniformly continuous on [a,b]. Then, there exists an ε>0 such that for every δ>0, there are x,y∈[a,b], depending on δ, such that |x−y|<δ and |f(x)−f(y)|≥ε. |
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