[See Steps] (a) Suppose that x_n and y_n converge to the same point. Prove that x_n-y_n→ 0 as n→ ∞ . (b) Show that the converse of part
Question: (a) Suppose that \(\left\{ {{x}_{n}} \right\}\) and \(\left\{ {{y}_{n}} \right\}\) converge to the same point. Prove that \({{x}_{n}}-{{y}_{n}}\to 0\) as \(n\to \infty \).
(b) Show that the converse of part (a) is false.
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(See Steps) Suppose that, x_n≥ 0 and x_n→ x, as n approaches
(Steps Shown) In the statement of the nested intervals property,
![[See] Show that that NIP might not](/images/solutions/MC-solution-library-62819.jpg "[See] Show that that NIP might not hold if")
[See] Show that that NIP might not hold if "bounded’ is
(Steps Shown) Prove than any real sequence x_n that satisfies
(See Steps) Prove that every closed bounded interval is sequentially
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