# Homework Help: Decimal Expansion, 1-1 onto

1. Sep 14, 2010

### kathrynag

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

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

3. The attempt at a solution
I don't even know where to begin. The whole decimal expansion business has me confused.

2. Sep 14, 2010

### kathrynag

Oops, I made a typo. That (0,1) in S should have been a (x,y).

3. Sep 15, 2010

### Staff: Mentor

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. Sep 15, 2010

### kathrynag

Yeah, that's what I meant.

5. Sep 15, 2010

### Staff: Mentor

(.5, .25) is in S, right? .5205 is in (0, 1).

6. Sep 15, 2010

### kathrynag

yeah. Ok, so then we have z=x1y1x2y2....