\centering、\align* 的间距误差

\centering、\align* 的间距误差

我正在写这个证明,但是几行较小的评论似乎有些奇怪——尽管它们应该用换行符隔开,但它们最终却居中并重叠了:

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这是另一个具有正确格式的块的示例(仅更改\align*括号之间的块和值):

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以下是受影响行周围的注释的源代码:

Prove that in any set of $n$ numbers, there exists at least one number less than or equal to the mean.
\begin{proof}[Proof.]
Assumption($\neg S$): all numbers in set S are greater than the mean.

Suppose set $S = \newset{x_{1}, x_{2},\dots,x_{n}}$. Then the mean is $\frac{x_{1}+x_{2}+\dots+x_{n}}{n}$.

If each $x_{i}, \forall i \in [1, n]$ is greater than the mean:
\begin{align*}
    x_{1} &> \frac{x_{1}+x_{2}+\dots+x_{n}}{n} \\
    x_{2} &> \frac{x_{1}+x_{2}+\dots+x_{n}}{n} \\
    &\vdots \\
    x_{n} &> \frac{x_{1}+x_{2}+\dots+x_{n}}{n} 
\end{align*}

Get the sum of both sides of the inequality, we get $\newset{x_{1}, x_{2},\dots,x_{n}} > \newset{x_{1}, x_{2},\dots,x_{n}}$. % affected line 
\centering\small{Contradiction: No number (and thus follows, set of numbers) is greater than itself.} \par % affected line
$\neg S$ (each element in set $S$ is greater than the mean) is clearly false; because of this, $S$ must be true.
\[\therefore \text{In a set of n numbers, there is at least one number less than or equal to the mean.}\]
\end{proof}

有人知道为什么会发生这种情况以及如何补救吗?谢谢!

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