The set $M$ of integers greater than or equal to eight can be written in set-builder notation as:

$M = \{ x \in \mathbb{Z} \mid x \geq 8 \}$

This denotes the set of all integers $x$ such that $x$ is greater than or equal to 8.

Would you like further clarification on this or an explanation of the symbols?

Here are some related questions to explore:

1. How can we represent a set of integers less than a given value?
2. How does set-builder notation differ from roster notation?
3. Can you combine multiple conditions in set-builder notation?
4. How would you write a set of real numbers in set-builder notation?
5. What are the key differences between sets of integers and subsets of real numbers?

Tip: When using set-builder notation, always define the domain of the variable explicitly, e.g., $x \in \mathbb{Z}$.