# Is there a better way to write it?

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.

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 $\alpha \neq \gamma$.

• The last sentence is best put as a (polite) comment in the post.
– Pedro
Jul 10, 2013 at 2:29
• Ah, you're right, @Peter. Paul, no disrespect intended.
– MTS
Jul 10, 2013 at 2:32
• 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! Jul 10, 2013 at 9:21
• Fixed to reflect both comments.
– MTS
Jul 10, 2013 at 12:39

In this case you can legitimately avoid having to write much English at all:

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

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 $\alpha<\mathfrak c$, $x(\alpha)=0$.
• Thnaks for your recomment. But I hope that i can write it in a sentence, because I used it in a proof.
– Paul
Jul 10, 2013 at 2:12
• @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. Jul 10, 2013 at 2:15