Matter /CAN/ be created!

[Lukeje]

I'll be blunt- 1/3 does not QUITE equal .333... (and by proxy, 2/3 doesn't quite equal .666...), that's just as close as we can come to measuring it since we can't write something to the infinity decimal place. (unless you've found a way that I don't know about, which no offense, but I highly doubt)

It's easy to write something that repeats to an infinite number of decimal places. There have been examples throughout the thread. Unless you mean writing out `long-hand' in which case the fact that you can't is kind of the point. What's neat is that because of its repeating nature we can actually see how it behaves as the number of decimal places tends to infinity.

As ACman said, it's 8.999..., which is equal to 9.


EDIT: Actually I'm going to quote some comments off facebook from one of my former lectures on this topic;
"On a psychological level the presence of infinity is secondary -- the first hurdle is multiple representations for real numbers.
This particular confusion somehow doesn't come up with rational numbers -- since when did you hear anybody argue that 1/2 and 3/6 weren't the same number?"

Ermm... 8.(9) is a rational number; it can be written 9/1 (or 18/2, etc.).

 

[Maze1125]

Actually multiply 9 by .999r though and see what you come up with.

That's just a red herring, as I said before, you just grasping at statements made in the proof, rather than at the reasoning between those statements.
Yes, the proof says that 9x = 9 where x = 0.999..., but that claim is not just pulled out the air, it is deduced from the previous statements. You can't just attack the statement while ignoring the reasoning the produced it.

Anyway, here's a subtly different way of arriving and the same claim:

0.999... * 10 - 0.999... = 0.999... * 9

Agreed? I mean, that's pretty basic, if you take a number and multiply by 10, then take one lot of that number away, you've got the number multiplied by 9 instead.

0.999... * 10 - 0.999... = 9.999... - 0.999... = 9

0.999... * 9 = 8.999...

I should hope these are both clearly true too.

So, one side of the original equation equals 9, and the other equals 8.999..., also, we know from the first part that the two sides are also equal to each other.
Therefore 9 and 8.999... must also be equal.