0

My solution for this function is let 0 map to 1/2, 1 to 1/3, and then for any other values map them to that value + 1/2. Is this the correct solution for this mapping?

aspookyghost20
  • 41
  • Could you write your solution on the form $$\phi(x) = \begin{cases} \frac12 & x=0 \ \frac13 & x=1 \ \cdots & \text{otherwise} \end{cases}$$ – md2perpe Oct 13 '17 at 19:17

1 Answers1

0

That doesn't seem to make sense. If you take the case of $\frac{3}{4} \rightarrow \frac{3}{4} + \frac{1}{2}$ you appear to get something not in the co-domain.

On the other hand, you can do the following. Consider the sequence

$\frac{1}{2},\frac{1}{3},\frac{1}{4},...$

You can construct a map which maps every element not in this sequence to itself, but every element in this sequence to a particular element allowing you to construct a bijection. For hints see the comments, and in particular the question which this is almost a duplicate of, but technically not quite.

Matt
  • 3,446
  • Ok so I could map that sequence to the addition of 1/2, but then leave the others the same? – aspookyghost20 Oct 13 '17 at 19:22
  • No. See the link to the almost duplicate question as I suggested, and perhaps you will be enlightened. How do you mean map the sequence to the addition of 1/2? – Matt Oct 13 '17 at 21:38