1/3 as a faction will always be 1/3, and 3 of them will be 1. However fractions shown as a decimal number will often be inaccurate. In the case of 1/3 being 0.333(recurring), the idea that 3 of those equals 0.999(recurring) works on the numerical basis rather then the fractal basis. With the numerical idea, you can go as far as you like, but eventually you have to give up and round off the number.
Remember pai = 3.1415927, some people have taken it to many decimal places without finding an end, it's one of those numbers like the square root of 2 or phi all of which in theory cannot be shown perfectly accurately using any number systems we use, this is why we have signs or symbols for so many of these numbers, because their true values are still unknown.
Here's something else for you:
Many mathmaticians believe that you cannot divide a number by 0, truth is you can.
Consider this:
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/(10^-100000) = 10^100000
As you divide by smaller and smaller numbers you increase the result, so if you said that 0 is the infinitely smallest number in existence, therefore dividing by 0 would result in a value equal to infinity, the largest number in existence. Also, divide by infinity and you would get 0.
Quote: "0.9 recurring is infintely close to one, but not quite"
Following my theory, if 0.99(recurring) is infinately close to 1, and an infinately small number is 0, wouldn't it say that you actually have a value of 1 not 0.99(recurring)?
But then comes the question, how is that if you take the recurring 9's to infinity that you eventually get to 1 somewhere, even though all you're doing is adding a 9 in the next decimal place?
My final question: does it really matter?
I don't suffer from insanity:
I enjoy every minute of it!
