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How can we construct an example of a set contains $n$ real numbers, which numbers include the parameter alpha in interval $(0,1)$ (e.g., one of the real numbers may be in the form $a_1=1-\alpha$), and the sum of these n numbers is equal to one?

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  • $\begingroup$ So you want a set of real numbers $X=\{x_1,\ldots,x_n\}$ such that $x_i=\alpha\in(0,1)$ for some $1\leq i\leq n$ and $\sum_{k=1}^n x_k=1$? $\endgroup$ – Dave Nov 28 '17 at 14:19
  • $\begingroup$ If this is the case @Dave, then $x_{i} = 1/n; \, \forall 1 \leq i \leq n$ will serve the purpose, for any integer $n > 1$. $\endgroup$ – Nash J. Nov 28 '17 at 14:22
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    $\begingroup$ Not sure I follow. Take $x_1=\alpha$, and $x_i=\frac {1-\alpha}{n-1}$ for $i>1$. Is that good enough? $\endgroup$ – lulu Nov 28 '17 at 14:24

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