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Let $S$ be a group of all such values in the interval $[-1,1]$, which have the property that for the series $x_0, x_1, x_2, \ldots$, defined by equations $x_0=t, x_{n+1}=2 x_n^2-1$, there exists a positive integer $N$ such that $x_n=1$ for each $n \geq N$. Prove that there are infinitely many values in the group $S$.
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