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I'm writting something. However I'm not good at English writting.

Suppose that $X=D^\mathfrak c$. I want to express this :

Let $x$ be the unique point of $X$ such that $x(\gamma)=1$ and for any other $\alpha < \mathfrak c$, $x(\alpha)=0$.

Is there a better way to write it? Thanks.

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3 Answers 3

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I would write almost what you have written, but change the order at the end, so the sentence would read:

Let $x$ be the unique point of $X$ such that both $x(\gamma)=1$ and $x(\alpha) = 0$ for all $\alpha < \mathfrak{c}$ with $\alpha \neq \gamma$.

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  • $\begingroup$ The last sentence is best put as a (polite) comment in the post. $\endgroup$
    – Pedro
    Commented Jul 10, 2013 at 2:29
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    $\begingroup$ Ah, you're right, @Peter. Paul, no disrespect intended. $\endgroup$
    – MTS
    Commented Jul 10, 2013 at 2:32
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    $\begingroup$ not for any $\alpha < \mathfrak{c}$, but for all $\alpha < \mathfrak{c}$ with $\alpha \neq \gamma$. Or else you'd define $x(\gamma) $ to be $0$ and $1$ at the same time! $\endgroup$ Commented Jul 10, 2013 at 9:21
  • $\begingroup$ Fixed to reflect both comments. $\endgroup$
    – MTS
    Commented Jul 10, 2013 at 12:39
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In this case you can legitimately avoid having to write much English at all:

Define $x\in X$ by $$x(\xi)=\begin{cases}1,&\text{if }\xi=\gamma\\0,&\text{otherwise}\;.\end{cases}$$

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I would recommend a list using enumerate.

Let $x$ be the unique point of $X$ such that:

  1. $x(\gamma)=1$, and
  2. For any $\alpha<\mathfrak c$, $x(\alpha)=0$.
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  • $\begingroup$ Thnaks for your recomment. But I hope that i can write it in a sentence, because I used it in a proof. $\endgroup$
    – Paul
    Commented Jul 10, 2013 at 2:12
  • $\begingroup$ @Paul: You can write the suggestion of this answer verbatim in a proof; there's nothing wrong with it and in fact it's better than your original formulation. $\endgroup$ Commented Jul 10, 2013 at 2:15

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