Final answer:
The set of all real numbers between 4 and 6, including 4, is expressed in set-builder notation as 4 ≤ x < 6, which includes all numbers equal to or greater than 4 but less than 6.
Step-by-step explanation:
To express the set of all real numbers between 4 and 6, including 4, in set-builder notation, we use the following expression:
x ∈ ℝ
This notation reads as "the set of all x such that x is a real number (represented by ℝ) and x is greater than or equal to 4 and less than 6". The symbol ∈ signifies 'belongs to', the vertical bar (|) stands for 'such that', and ℝ denotes the set of all real numbers. By including the equal sign with the 4, we are specifying that 4 is a part of the set, while the lack of an equal sign with the 6 indicates that 6 is not included in the set. This set includes all real numbers like 4.1, 5, 5.999, and so on, up to but not including 6.