1
$\begingroup$

The problem is, "Let $S$ be a set of $3$, not necessarily distinct, positive integers. Show that one can transform $S$ into a set containing $0$ by a finite number of applications of the following rule: Select two of the three integers, say $x$ and $y$, where $x

My question is: If $y>x$, then $y-x \neq 0$ and therefore, is there no solution to this problem? Did the writers mean $x\leq y$ or am I making a mistake? If so, can someone please clarify what is meant in the question? Thank you!

  • 1
    What happens if two of your numbers are 2 and 4? Isn't it possible to keep ending up with 4 and 2? – 2017-02-08
  • 2
    Your reasoning looks right to me. Perhaps a simpler way to put it: if S is (1,1,1) then as stated there are no permissible moves. – 2017-02-08
  • 2
    $x\le y$ would look much more reasonable in this problem. Maybe there's a typo in the source or in the process of copying the text of the problem? – 2017-02-08
  • 0
    I agree that they probably meant $\leq$. Otherwise, since the numbers are specifically not necessarily distinct, we wouldn't be able to do anything with $S = \{1, 1, 1\}$. – 2017-02-09

0 Answers 0