Solution Found!
Show that if S is a set, then there does not exist an onto
Chapter 2, Problem 40E(choose chapter or problem)
QUESTION:
Show that if S is a set, then there does not exist an onto function f from S to the power set of 5. Conclude that |S|< This result is know n as Cantor’s theorem. [Hint: Suppose such a function f existed. Let T = {s ? S | s? f{s)) and show that no element s can exist for which f(s) = T.]
Questions & Answers
QUESTION:
Show that if S is a set, then there does not exist an onto function f from S to the power set of 5. Conclude that |S|< This result is know n as Cantor’s theorem. [Hint: Suppose such a function f existed. Let T = {s ? S | s? f{s)) and show that no element s can exist for which f(s) = T.]
ANSWER:Solution:Step 1 :In this problem we have to prove that if is a set, then there does not exist a