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### The limit of infinite product $\prod_{k=1}^{\infty}(1-\frac{1}{2^k})$ is not 0?

Is there any elementary proof that the limit of infinite product $\prod_{k=1}^{\infty}(1-\frac{1}{2^k})$ is not 0?
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### Convergence of an infinite product $\prod_{k=1}^{\infty }(1-\frac1{2^k})$? [duplicate]

Problem: I want to prove that the infinite product $\prod_{k=1}^{\infty }(1-\frac{1}{2^{k}})$ does not converge to zero. It doesn't matter to find the value to which this product converges, but I am ...
$\lim_{n\to\infty} (1-\frac{1}{2})(1-\frac{1}{4}) \cdots (1-\frac{1}{2^n})=\prod_{n=1}^{\infty} (1-\frac{1}{2^n})$ I've tried this techniques: 1) Using squeeze theorem, but i had not find right ...