Let R denote the real numbers and R+ the positive real numbers. Addition is a binary
Chapter 8, Problem 23(choose chapter or problem)
Let R denote the real numbers and R+ the positive real numbers. Addition is a binary operation on R, and multiplication is a binary operation on R+. Consider [R, +] and 3R+, # 4 as mathematical structures. a. Prove that the function f defined by f(x) = 2x is a bijection from R to R+. b. Write the equation that an isomorphism from [R, +] to 3R+, # 4 must satisfy. c. Prove that the function f of part (a) is an isomorphism from 3R, + 4 to 3R+, # 4. d. What is f 1 for this function? e. Prove that f 1 is an isomorphism from 3R+, # 4 to [R, +]
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer