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Meaning of |x – a | < δ.

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|x – a | < δ = (x – a) < δ if x ≥ a

or = x < (a + δ) if x ≥ a

= (a – x) < δ if x < a

or = x > (a – δ) if x < a

∴ |x – a| < δ ⇔ x ∈ (a- δ, a + δ)

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