Write each of the following sets in set- builder form :
H= {.}

Answer

To write the set \( H = \{.\} \) in set-builder form, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Element**: The set \( H \) contains only one element, which is a dot (.). In mathematical terms, this dot can represent a number.

2. **Interpret the Dot**: The dot (.) is commonly used to denote a decimal point. In this context, it can be interpreted as the number zero (0). This is because a dot on its own can be seen as representing the decimal point in the number 0.0, which is simply 0.

3. **Set Representation**: Now that we have established that the dot represents the number 0, we can express the set \( H \) in terms of a variable \( x \).

4. **Write in Set-Builder Form**:
- We denote the variable as \( x \).
- We state that \( x \) is a number.
- Since \( H \) contains only the element 0, we can write:
\[ H = \{ x \mid x = 0 \} \]

### Final Answer:
Thus, the set \( H \) in set-builder form is:
\[ H = \{ x \mid x = 0 \} \]