Define an equivalence relation on R² by: ¤1, Y1) ~ (x2, Y2) e if and only if (*1, Yı) and (x2, Y2) have the same distance from the origin. (a) Interpret the equivalence classes geometrically and describe the quotient R²/ ~. (b) Is the function f: (R°/ ~) → R, [(21, yn)] → 국+ yf well defined?
Define an equivalence relation on R² by: ¤1, Y1) ~ (x2, Y2) e if and only if (*1, Yı) and (x2, Y2) have the same distance from the origin. (a) Interpret the equivalence classes geometrically and describe the quotient R²/ ~. (b) Is the function f: (R°/ ~) → R, [(21, yn)] → 국+ yf well defined?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...
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