proof that 0.999 … = 1 and that it isn’t

That it is:

• If x = 0.999 … , 10x = 9.999 …, 9x = 10x – x = 9 therefore x=1 = 0.999 …
• 1/3 = 0.333 …, 2/3 = 0.666 …, therefore 3/3 = 1 = 0.999 …

That it isn’t:

• Look, let’s do the whole thing, then do it again, only replacing the 0.999 … with 1. So x=1, 10x=10, 9x=9, x=1: 1=1. We know that!!!!
• So apparently, 0.000000 … 1 is 0, right? But what if people had more common sense and said that the number of zeroes were countable? Then 0.000000 … 1 wouldn’t be 0. So 1- 0.99999999 … 9 = 0.000000 … 1, and that is a number that is greater than 0, so there IS a difference.

Bye!