Determine if each function is one-one.
To each country in the world assign the latitude and longitude of its capital.

Answer

To determine if the function that assigns the latitude and longitude of each country's capital is one-one, we can follow these steps:

### Step 1: Understand the Definition of a One-One Function
A function is considered one-one (or injective) if every element in the domain maps to a unique element in the codomain. In other words, no two different inputs (in this case, countries) can map to the same output (latitude and longitude).

### Step 2: Identify the Domain and Codomain
In this scenario:
- **Domain**: The set of all countries in the world.
- **Codomain**: The set of all possible latitude and longitude pairs.

### Step 3: Analyze the Mapping
Each country has a unique capital city, and each capital city has a specific latitude and longitude associated with it. Therefore, when we assign the latitude and longitude of a capital to its corresponding country, we are creating a mapping from countries to their capitals' coordinates.

### Step 4: Check for Uniqueness
Since each country has a distinct capital, and each capital has a unique latitude and longitude, this means:
- No two countries share the same capital.
- Thus, no two countries will have the same latitude and longitude assigned to them.

### Step 5: Conclusion
Since every country maps to a unique latitude and longitude, we conclude that the function is one-one.

### Final Answer
The function that assigns the latitude and longitude of each country's capital is a one-one function.

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