ok some key points about infinity ot address here :) >then the remainder disappears, for unexplained reasons. Actually no - it doesnt disappear. That's why it

ok some key points about infinity ot address here :) >then the remainder disappears, for unexplained reasons. Actually no - it doesnt disappear. That's why it works. Dont forget the definition of infinity is "forever". The remainder is always there - and it always reduces further (edit: if you continue completing the sum. As you can see below the sum is already completed for infinite length anyway - your just manually bound checking it at the beginning) In your counter argument where the 0.0....1 acts as a remainder. The set of 0's before the 1 can only be finite. One reason people fall for this is because they imagine the infinite set growing by adding a 0 on the end each time. Or perhaps pushing on one the front (which is what would have to happen for your requirement). This is *wrong( entirely - the infinite set exists, in entirety for the whole of it's infinity.