Decimal Expansion, 1-1 onto

In summary, the conversation discusses finding a 1-1 function that maps a set S into the interval (0,1) using the fact that every real number has a decimal expansion. The function is then evaluated for its onto property and there is a clarification about the definition of S.
  • #1
kathrynag
598
0

Homework Statement


Use the fact that every real number has a decimal expansion to produce a 1-1 function that maps S into (0,1). Discuss whether the formulated function is onto.


Homework Equations



S={(0,1):0<x, y<1}

The Attempt at a Solution


I don't even know where to begin. The whole decimal expansion business has me confused.
 
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  • #2
Oops, I made a typo. That (0,1) in S should have been a (x,y).
 
  • #3
Just to be clear, S is the quarter plane whose left edge is the y-axis and whose upper edge is the line y = 1, right?

Or did you mean that both x and y are between 0 and 1? If that's what you meant, your description for S should have been written as S = {(x, y) | 0 < x < 1, 0 < x < 1}.
 
  • #4
Mark44 said:
Just to be clear, S is the quarter plane whose left edge is the y-axis and whose upper edge is the line y = 1, right?
Yeah, that's what I meant.
 
  • #6
yeah. Ok, so then we have z=x1y1x2y2...
 

1. What is decimal expansion?

Decimal expansion is the representation of a number in decimal form, using a decimal point and digits to the right of the point to indicate fractions of a whole number.

2. What does it mean for a function to be 1-1 onto?

A function is 1-1 onto, also known as a bijective function, when every element in the domain of the function is paired with exactly one element in the range, and every element in the range has at least one corresponding element in the domain.

3. How is decimal expansion related to 1-1 onto functions?

Decimal expansion is used to represent the input and output values of a 1-1 onto function. The decimal expansion of the input represents the domain, and the decimal expansion of the output represents the range of the function.

4. What is an example of a 1-1 onto function with decimal expansion?

An example of a 1-1 onto function with decimal expansion is f(x) = 2x + 3. For any input value x, the output value will be unique and the function is bijective. The decimal expansion of the input and output values will also show the one-to-one correspondence.

5. Why is understanding decimal expansion and 1-1 onto functions important in science?

Understanding decimal expansion and 1-1 onto functions is important in science because many scientific processes and phenomena can be represented and analyzed using functions. By understanding these concepts, scientists can better interpret and manipulate data to make accurate predictions and draw meaningful conclusions.

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