If 0.999(etc) = 1, does 1 - 0.999 go to zero?

[pocaracas]

I always thought that x-dx != x, but you guys seem to be onto something.... .... ....
It seems dx is much larger than 0.000(etc)1.

PS: x is a real number; dx is an infinitesimal part of x.
!= means "not equals"

[Aractus]

0.000(etc)1 isn't a number.

[LastPoet]

Yep, you cannot have 0.00(infinity)1.

[Waratah]

Is 0.999...(infinity)1 a number?
if not why?

If it is a number would it = 1 as well since if:

x = 0.999...1
10x = 9.999...1
10x - x = 9.999...1 - 0.999...1
9x = 9
x = 1

[Tiberius]

Is 0.999...(infinity)1 a number?
if not why?

If you're dealing with infinitesimals, then you can get numbers between 0.999... and 1. However, in standard arithmetic / calculus, they don't exist. You only really get them when dealing with hyperreals or surreals.

It should be obvious why 0.999...1 isn't a number. The "..." signifies that the last set of numbers repeats to infinity. So the last 9 is repeating.

What 0.999...1 therefore says is that you have an infinite string of 9's after the decimal point...and then a 1.

Well, that just doesn't make any sense. You can't have an infinite string of 9's followed by anything. If something is infinitely long, it doesn't have an end. There is nowhere to place your 1, because doing so would end the number...making it finite.

Your calculation doesn't make sense in this respect either.

[Aractus]

Anything you put after infinity is meaningless. ∞ + 1 = ∞. ∞ + ∞ = ∞. ∞ * ∞ = ∞, and even ∞/∞ = ∞. ∞ itself isn't a number either, hence why it doesn't follow the rules of numbers. But you can have irrational numbers, and you can also have fractions. 1/3 is a fraction, it's equal to 0.333... which is a rational number. An irrational number is a number that cannot be represented as a fraction. For instance Pi. Pi has ∞ decimal places, and for any Nth decimal there is a value (0-9). There is no N = ∞ + 1 decimal place of Pi, nor could you calculate it.

To get back to your point, to be able to have x = 0.000...1 you would need to be able to solve the equation:

1/∞ = x. This of course is impossible, there is no value for x where x∞ = 1. giving x the value of 0 leads 0∞ = 0, giving x any other positive value x∞ = ∞.

[Tiberius]

This is a good video on the subject:

http://www.youtube.com/watch?v=TINfzxSnnIE

[pocaracas]

Right y'all are, except:

even ∞/∞ = ∞.

This one depends on how much the upper ∞ is greater or smaller than the lower one.

lim (x-> ∞) x^2/x = ∞
lim (x-> ∞) x/x^2 = 0
lim (x-> ∞) sqrt(x^2)/x = 1

[Tiberius]

Lim means as x approaches infinity, the answer approaches...(some value).

X is not set to infinity if I recall correctly.

[pocaracas]

There are some infinities greater than other infinities.
#N < #R