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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
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
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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.  

Is your fonto? Justify your answer.
Transcribed Image Text: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.
Transcribed Image Text: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.
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