5 ms·

Thanks, this is actually a much better description, especially 4. OP's description can be used to "prove" that 1/2 is irrational.

• thaumasiotes 4y ago
  > OP's description can be used to "prove" that 1/2 is irrational. That won't work; in that case, k' will not be a positive number (k/2 - k is negative whenever k is positive), so you'll fail to produce a contradiction.
  • rhn_mk1 4y ago
    Fair enough. Take 3/2 in that case.
    • hgsgm 4y ago
      Doesn't work, because in k * (3/2 - 1)(3/2) = k'(9/4) - k(3/2) (3/2)^2 = 9/4 is not an integer, you don't get k' < K so there is no contradiction. You'd only get an integer if 4 divides k', which doesn't happen, because k = 2 and k' = k(3/2 -1) = k/2 = 1
      • rhn_mk1 4y ago
        Thanks, you're right. I missed that there was supposed to be a √2*√2 in the expansion of the last line.