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Home Limits, Analytic Geometry, and Approximations The ε, δ Condition for Limits Corollary  
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Corollary
COROLLARY The following are equivalent.
whenever x  c < δ, f(x)  f(c) < ε. PROOF Both (i) and (ii) are equivalent to lim_{x→c }f(x) = f(c). Intuitively, this corollary says that f is continuous at c if and only if f(x) is close to f(c) whenever x is close to c.


Home Limits, Analytic Geometry, and Approximations The ε, δ Condition for Limits Corollary 