# How many times can a piece of paper be folded in half?

What is the maximum number of times a piece of paper (of non-zero thickness) can be folded in half (mathematically)?

Edit:
I totally forgot to mention the "non-zero thickness" part; I've now included it.

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Mathematically, if you're modelling the paper as just an infinitely thin plane, you can fold it infinitely often. If you're referring to actual paper, then this is entirely dependent on the physical properties of paper, and it's not really a math question. – Adrian Petrescu Jan 16 '11 at 19:29
Are you asking about "physical" or "mathematical" limitations? – user1736 Jan 16 '11 at 19:29
"Mathematical" limitations. I'll make the edit. – iamsid Jan 16 '11 at 19:31

The zero thickness model is a bad model. For nonzero thickness the problem was studied by Britney Gallivan, who derived an upper bound on the number of folds based on the thickness and dimensions of the paper. The current world record for actual paper was set by her; it's $12$. There are some additional details and references at her Wikipedia article.
Theoretically you can fold the paper into half infinite number of times since $1 - (\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots) = 0$. However, practically the number of times you can fold the paper into half will depend on the dimensions of the paper (length, breadth and thickness), the stiffness of the paper, and more importantly your patience and mechanical strength to keep folding it.