Is there a better way to write it?

Question

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.

Answer 1

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 $\alpha \neq \gamma$.

Answer 2

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

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

Answer 3

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 $\alpha<\mathfrak c$, $x(\alpha)=0$.