HOOORAY THIS BLOODY THREAD AGAIN!!! And they said the old Flood was dead. The problem is that 0.9... is not the same kind of number that 1 is. 0.9... has an infinity in it (an infinite number of 9s after the decimal point) and is therefore impossible to definitively write down and deal with properly. Believe it or not this whole argument stems from the problem that you can't write infinity down. We use symbols and ellipses to get around having to write an infinite number down, but does an inability to write it down directly, affect the methods of calculation? Using symbols that merely [i]infer[/i] infinity rather than using infinity itself seems almost dishonest in the usually quite direct world of maths. Is it not dishonest to use finite symbols to express infinity? I would argue that it is; by putting infinity into a box you have made it finite and therefore anything you do to it affects the finite box only, not the infinity it represents. You necessarily can't deal with the infinity, that's why you boxed it up, but in boxing the infinity up you lost it. You can't put a pot of river water over a fire and claim you're boiling the whole river. If the number of 9s was finite then it could be written down and it would be demonstrably unequal to 1; as it is though, there is no way to mathematically prove they are different numbers because the distance between them can never actually be defined as it is forever shrinking. But that does not mean the distance between them just isn't there. Mathematical jiggery-pokery or not, there is still an infinitely small gap between the numbers, hence why they are not written as the same. They may be 'essentially' the same, but they are not 'actually'. Edit: On second thoughts I probably shouldn't have come to a conclusion either way given the first bit.