i always ,,loved'' the variation that goes like: if 0.99... != 1, then there has to be an x that 0.99.... + x = 1.0 (or to say 1 - 0.99.. > 0 must hold), so you

i always ,,loved'' the variation that goes like: if 0.99... != 1, then there has to be an x that 0.99.... + x = 1.0 (or to say 1 - 0.99.. > 0 must hold), so you can start to find this x (as 0.01, 0.001, 0.0001, etc.) and fail of course. this is not so ,,simple'' as your examples (or the (10*0.99.. - 0.99..)/9) but lights the point where most people go wrong here (at least for me)