Is your fonto? Justify your answer. Find a 1-1 function f : (0, 1) × (0, 1) → (0, 1). (Hint: use decimal expansions of numbers in (0, 1). Make sure to take care of the non-uniqueness of decimal presentations of real numbers.) Given: f: (0,1) x (0,1) → (0,1) Let x = 0 x_{1}x_{2}x_{3}x_{4} ... = (0,1) y=0 y_{1} y_{2} y_{3} y_{4} ... = (0,1) Then we define f(x,y) = 0 ⋅ x_{1} y_{1}x_{2} y_{2}x_{3} y_{3} € (0,1) Hence, this function is one to one function and the value (0 · x_{1} y_{1} x_{2} y_{2} x_{3} y_{3}...) covers all values between (0,1). So this means that the function is also onto.
Is your fonto? Justify your answer. Find a 1-1 function f : (0, 1) × (0, 1) → (0, 1). (Hint: use decimal expansions of numbers in (0, 1). Make sure to take care of the non-uniqueness of decimal presentations of real numbers.) Given: f: (0,1) x (0,1) → (0,1) Let x = 0 x_{1}x_{2}x_{3}x_{4} ... = (0,1) y=0 y_{1} y_{2} y_{3} y_{4} ... = (0,1) Then we define f(x,y) = 0 ⋅ x_{1} y_{1}x_{2} y_{2}x_{3} y_{3} € (0,1) Hence, this function is one to one function and the value (0 · x_{1} y_{1} x_{2} y_{2} x_{3} y_{3}...) covers all values between (0,1). So this means that the function is also onto.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 1E
Related questions
Question
Could you please help me with this question? the question is asking if my f is also onto. I have attached the problem with my answer that has to do with the question that is being asked.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage