Let f: (0,1)→ R be a function and let a € (0,1). Match each statement in Group A with a statement from Group B which means the same thing. Group A: (i) Ve > 0,36 >0 such that |x-a| < 8 implies |ƒ(x) = f(a)| < €. (ii) €0, 0, x − a| < 8 implies [ƒ(x) − f(a)| < €. (iii) >0 such that V6 > 0, |x − a| < 8 implies |ƒ(x) − ƒ(a)| < €. (iv) 3€ >0 and 36 >0 such that |x − a| < 8 implies [ƒ(r) – f(a)| < €. (v) 0,3€ > such that |x − a| < 6 implies |ƒ(x) - f(a)| < €. (vi) 36 >0 such that Ve > 0, |x − a| < 6 implies |ƒ(x) - f(a)| < €. Group B: (a) f is continuous at a. (b) f is bounded on (0, 1). (c) f is constant on (0,1) (d) There is some neighbourhood of a on which f is bounded. (e) There is some neighbourhood of a on which f is constant.
Let f: (0,1)→ R be a function and let a € (0,1). Match each statement in Group A with a statement from Group B which means the same thing. Group A: (i) Ve > 0,36 >0 such that |x-a| < 8 implies |ƒ(x) = f(a)| < €. (ii) €0, 0, x − a| < 8 implies [ƒ(x) − f(a)| < €. (iii) >0 such that V6 > 0, |x − a| < 8 implies |ƒ(x) − ƒ(a)| < €. (iv) 3€ >0 and 36 >0 such that |x − a| < 8 implies [ƒ(r) – f(a)| < €. (v) 0,3€ > such that |x − a| < 6 implies |ƒ(x) - f(a)| < €. (vi) 36 >0 such that Ve > 0, |x − a| < 6 implies |ƒ(x) - f(a)| < €. Group B: (a) f is continuous at a. (b) f is bounded on (0, 1). (c) f is constant on (0,1) (d) There is some neighbourhood of a on which f is bounded. (e) There is some neighbourhood of a on which f is constant.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 3E: 3. For each of the following mappings, write out and for the given and, where.
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