Originally Posted by jhawkkw
This as written is correct, but fails to take into account that .999... a number of infinite length.
Actually words 7 and 9 of my post take this into account when combined with the rest of the first sentence
If you look how your maths is written, you have .9999 ad infinitum but when you multiply it by 10, you magically have add infinitum + 1 extra digit, which is why your maths looks to work. But we all know .99999 blah is not actually 1.
Since infinity isn't really a number, it can't really be used in maths to form any cohesive proof that 1 isn't 1.
If you massage numbers correctly, you can "prove" anything and you did a good job of massaging them. Well done. But joking aside, .9 reoccurring is nothing except what it is, even if you can make it appear so on paper. Maths is the last bastion of comedy.