I is the set of integers. Deseribe the following relations in words, giving its domain and range.
`{(0,0),(1,-1),(2,-2),(3,-3)......}`

Answer

To describe the given relation `{(0,0),(1,-1),(2,-2),(3,-3),...}` in words, we will identify its domain and range step by step.

### Step 1: Identify the Pattern in the Relation
The relation consists of pairs where the first element is a non-negative integer (0, 1, 2, 3, ...) and the second element is the negative of the first element. For example:
- When the first element is 0, the second element is 0.
- When the first element is 1, the second element is -1.
- When the first element is 2, the second element is -2.
- When the first element is 3, the second element is -3.
- This pattern continues indefinitely.

### Step 2: Determine the Domain
The domain of a relation is the set of all possible input values (first elements of the ordered pairs). In this case, the first elements are the non-negative integers starting from 0. Therefore, the domain can be expressed as:
- **Domain**: {0, 1, 2, 3, ...} or in interval notation as [0, ∞).

### Step 3: Determine the Range
The range of a relation is the set of all possible output values (second elements of the ordered pairs). In this case, the second elements are the negatives of the first elements. Therefore, the second elements are:
- When the first element is 0, the second element is 0.
- When the first element is 1, the second element is -1.
- When the first element is 2, the second element is -2.
- When the first element is 3, the second element is -3.
- This pattern continues indefinitely in the negative direction.

Thus, the range can be expressed as:
- **Range**: {0, -1, -2, -3, ...} or in interval notation as (-∞, 0].

### Final Description
In words, the relation consists of pairs where the first element is a non-negative integer and the second element is the negative of the first element. The domain of this relation is the set of all non-negative integers (including 0), and the range is the set of all non-positive integers (including 0).

### Summary
- **Domain**: [0, ∞)
- **Range**: (-∞, 0]