Say we want to know what 0.9999..^2 is, now, already, intuition tells you that this is not equal to 1, because it isn't. To find out what this is equal to, let's find 0.9^2 first, what is 0.9^2? That's right, it's 0.81, now, the derivative of the graph x^2 when x = 0.9 is 1.8, now, as x will increase by 0.09999.., we can multiply this change in x by the derivative to find out what 0.999..^2 will be, so, 0.9999..^2 = 0.81 + (1.8*0.09999...), now, this clearly isn't going to be equal to 1, even if i please the one fags and assume 0.09999.. = 0.1, I get that 0.999..^2 = 0.99