Assume that for a∈R and f:R→R ∀ϵ>0∃δ>0∀x such thah f(x)−f(a)∣<ϵ we have ∣x−a∣<δ.  Does it follow that f(x) is continuous

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answerhappygod
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Assume that for a∈R and f:R→R ∀ϵ>0∃δ>0∀x such thah f(x)−f(a)∣<ϵ we have ∣x−a∣<δ.  Does it follow that f(x) is continuous

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Assume that for a∈R and f:R→R ∀ϵ>0∃δ>0∀x such thah f(x)−f(a)∣<ϵ we have ∣x−a∣<δ.  Does it follow that f(x) is continuous at a ? What can be said about the function f(x) ?
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