Re:More fun... (Score 1)

Indeed the above proof is circular, because you assume in step 3 that the difference between 1 - 0.999... and 10 - 10*0.999... is the same. In some forms of non-standard analysis, you can assume without contradiction that there is some w (should be omega but slashdot does not allow this character) with 0.999... = 1 - 1/w.