Is Every Real Number's Decimal Expansion Key to Mapping S into (0,1)?

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Homework Help Overview

The discussion revolves around the mapping of a set S, defined in relation to the interval (0,1), using the decimal expansion of real numbers. Participants are exploring the implications of this mapping and whether the function can be onto.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express confusion regarding the concept of decimal expansions and how they relate to the mapping. There are questions about the correct definition of the set S and its boundaries. Some participants attempt to clarify the nature of S and its elements.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the definitions and properties of the set S. There is an acknowledgment of the need to understand the mapping function better, but no consensus has been reached on its properties or implications.

Contextual Notes

There are indications of potential typos and misunderstandings regarding the definition of S, which may affect the discussion. The specific constraints of the homework problem are not fully articulated, leading to varied interpretations among participants.

kathrynag
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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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Oops, I made a typo. That (0,1) in S should have been a (x,y).
 
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}.
 
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.
 
(.5, .25) is in S, right? .5205 is in (0, 1).
 
yeah. Ok, so then we have z=x1y1x2y2...
 

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