I'm very confused about this question. I would like to check if i'm correct or not.


For each $n \in \mathbb{N}$ be $ D_n = (0, {1 \over n})$, where $(0, {1 \over n})$ represents the open interval which extremes are $0$ and ${1 \over n}$. Define the difference between $D_3 - D_{20}$

My solution:

enter image description here

I tried to put the sets in a Venn Diagram to make it clear but sincerely i got even more confused.

Thanks in advance.

  • 3
    $\begingroup$ If you want a diagram, then some scattered fractions aren't the way to go. $D_n$ is an interval. Draw the interval $D_3$ and the interval $D_{20}$; do you understand what these two sets are individually? $\endgroup$
    – user296602
    Sep 25 '18 at 19:20
  • $\begingroup$ Hm... i think i can draw a line to represent these intervals. First is 0 -> 0,33 and the second is 0 -> 0,05 correct? $\endgroup$
    – joann2555
    Sep 25 '18 at 19:23
  • $\begingroup$ Yes, with the caveat that there is no reason to bring decimals into this. $\endgroup$
    – user296602
    Sep 25 '18 at 19:23
  • 1
    $\begingroup$ You are off by one point in the last. $\endgroup$ Sep 25 '18 at 19:26
  • 1
    $\begingroup$ Hm. It got me. In fact 1/20 is in the set, right? So the final answer should be: [ 1/20, 1/3[ $\endgroup$
    – joann2555
    Sep 25 '18 at 19:32

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