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• Mathematical induction is a method of proof used to establish that a given statement is true for all natural numbers. Let S(n) be a statement about the positive integer n. If
• Let f : D → ℝ and let c ∈ D. We say that f is continuous at c if for every ε > 0 there exists a δ > 0 such that $\left| {f\left( x \right) - f\left( c \right)} \right|\, < \,\varepsilon $ whenever and x ∈ D. If f is continuous at each point of a subset K ⊆ D, then f is said to be continuous on K. Moreover, if f is continuous on its domain...
• Let (ak) be a sequence of real numbers. We use the notation to denote the nth partial sum of the infinite series . If the sequence of partial sums (sn) converges to a real number s, we say that the series is convergent and we write ...
• We say A ⊂ ℝ is open if for every x ∈ A there exists ε > 0 such that (x − ε, x + ε) ⊆ A. A is closed if its complement Ac is open. Similarly a set A in a metric space (M,d) is called open if for each x ∈ A, there exists an ε > 0 such that B(x;ε) ⊂ A. Here,
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