In words, the notation $s(X) := X \cup \{ X \}$ can be described as follows:

• $X$ is a set.
• $\cup$ denotes the union operation in set theory, which combines the elements of two sets.
• $\{ X \}$ represents a new set that contains $X$ as its only element (i.e., the set containing the set $X$).

Thus, the expression $s(X) := X \cup \{ X \}$ defines a new set $s(X)$ as the union of the set $X$ with the set that contains $X$ as an element.

To summarize: The set $s(X)$ consists of all the elements of $X$, plus $X$ itself as an additional element.

Would you like a detailed example or further clarification?

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Here are 5 related questions you might consider:

1. What is the difference between $X \cup \{ X \}$ and $X \cup X$?
2. How does this definition relate to recursion in set theory?
3. Can this operation result in a set containing itself, and what are the implications of that?
4. What are some applications of this kind of set construction in mathematics?
5. How would $s(X)$ behave for specific sets, such as $X = \emptyset$ or $X = \{1, 2\}$?

Tip: When dealing with sets, always keep in mind the distinction between an element and a set containing that element!