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Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.

Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 40E
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Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.
Transcribed Image Text:Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.
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