Suppose A is a function that assigns to each subset of the plane a number in such a way that the following rules are satisfied: 1: A(X) > 0 for each X C R² 2: If X and Y are disjoint then A(X U Y) = A(X)+ A(Y). Prove that if X CY then A(X) < A(Y).
Suppose A is a function that assigns to each subset of the plane a number in such a way that the following rules are satisfied: 1: A(X) > 0 for each X C R² 2: If X and Y are disjoint then A(X U Y) = A(X)+ A(Y). Prove that if X CY then A(X) < A(Y).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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