Responding to SPP because he locked his comment, as usual

Since SPP, as usual, shows nothing but cowardice by replying and then denying anyone else the right to respond, I am forced to post this here, now.

> And everyone the hell knows that zero is never going to be encountered. You won't the hell encounter zero with scaling down of a non-zero number.

As long as n is an integer, you are correct.

But as long as n is an integer, 1-1/10^(n) ***does not*** equal 0.999.... You can check for yourself:

1 - 1/10^(1) = 1 - 0.1 = 0.9 1 - 1/10^(2) = 1 - 0.01 = 0.99 1 - 1/10^(3) = 1 - 0.001 = 0.999 1 - 1/10^(4) = 1 - 0.0001 = 0.9999 1 - 1/10^(5) = 1 - 0.00001 = 0.99999 1 - 1/10^(6) = 1 - 0.000001 = 0.999999 1 - 1/10^(7) = 1 - 0.0000001 = 0.9999999 1 - 1/10^(8) = 1 - 0.00000001 = 0.99999999 1 - 1/10^(9) = 1 - 0.000000001 = 0.999999999 1-1/10^(10) = 1 - 0.0000000001 = 0.9999999999

As you can clearly see, there is never, at any point, a situation where 1-1/10^(n) equals 0.999..., ever, so long as n is an integer. For *any* integer n, we never generate 0.999..., but rather something infinitely shorter than the genuine article.

But that means your arguments fail. You ***do not*** know that 0.999... is permanently less than 1, because you *do not get* 0.999... from ANY situation where 1-1/10^(n) is an integer. Never ever.

As soon as you can show me that an integer n is capable of giving you 0.999..., I will grant your position. What integer n gives you the ACTUAL 0.999..., and not some other number that stops?