Folding paper in half

How many times can you fold a piece of paper in half? If you have not thought about this before then your answer may be high, but the generally accepted number is 7 or 8. I find that I am stuck on 7. However if you have a piece of paper big enough then you can get more folds into it, but let's stick with the idea of folding an A4 piece of paper.

When you fold it in half you have the thickness of 2 sheets and half the original size. When you fold it again you have a thickness of 4 sheets and a quarter of the original size. On the third fold you have a thickness of 8 sheets and an eighth of the original size. Can you see the pattern? With each fold you double the thickness and half the size. So one fold in the paper produces a thickness of 2 sheets, and it is 1/2 the size. Two folds produce 4 sheets, and it is 1/4 size.

Now just with numbers; 2 and 1/2 , 4 and 1/4, 8 and 1/8, 16 and 1/16, 32 and 1/32, 64 and 1/64, 128 and 1/128. This is as far as I get. In a few seconds you can fold a piece of paper so that it is 1/128 of it's original size and it is 128 thicknesses of paper. Can you get the paper to be 256 times its original thickness?

That sums it up.