Do $\{x\mid x\in\mathbb{R},x<k\}$ and $\{x\in\mathbb{R}\mid x<k\}$ mean the same thing?

Question

Short question about set-builder notation.

Do $$D=\{x \mid x \in \mathbb{R}, x < k\}$$ and $$D=\{x \in \mathbb{R} \mid x < k\}$$ mean the same thing?

I see both of them used in different contexts and was wondering if they are interchangeable.

Answer 1

They mean the same thing. I prefer $\{x \in \mathbb{R} \mid x < k \}$, because it is a clear separation between the domain ($\mathbb{R}$) and the condition ($x < k$). So I think it is easier to read, definitely when the condition gets more complicated.