(March 17, 2011 at 5:02 pm)Tiberius Wrote: An "infinite" number is a number that has infinite value, whilst you are talking about numbers that have a finite value, but are infinitely long. That was the difference. 0.(1) is a finite number, as it has a finite value, but it is infinitely long.
As I've said before, 0.(0)1 is an invalid number; it can't exist. You cannot have an infinite number of 0's and then have a 1 on the end, because there can't be an end for the 1 to go on.
You know, I've been thinking of something...
if we've got a meter long segment, and we want to split it in 3 equal parts, the dimension of each part would be 0.(3) m.
That is:
we get a segment of a line, and want to get the first 1/3 of it. We call the new segment, that would be extracted, a:
We calculate 0.3 m from left and draw a line to it. here, a = "0.3 m";
We zoom and we add 0.03 to it. Now, a = "0.03 m". We've noticed that a has increased;
We zoom further and we add 0.003 to it. Now, a = "0.003 m". the length of a has increased again.
And this process would continue forever.
So, wouldn't this mean that the resulting segment a would be infinitely long?
And this would mean that a stick of 1 meter length can never be splat equally, because the stick is formed of atoms that have specific sizes (and you cannot split their protons, etc.). Right?
