Determine if each function is one-one.
To each person on the earth assign the number which corresponds to his age.

Answer

To determine if the function that assigns each person on Earth a number corresponding to their age is one-one, we can follow these steps:

### Step 1: Define the function
Let the function \( f \) be defined as follows:
- \( f: P \to A \)
- Where \( P \) is the set of all people on Earth and \( A \) is the set of ages.

### Step 2: Analyze the mapping
In this function, each person \( p \in P \) is assigned a number \( a \in A \) that corresponds to their age.

### Step 3: Identify the uniqueness of the mapping
For a function to be one-one (or injective), each element in the domain must map to a unique element in the codomain. This means that if two different people have the same age, they would receive the same number.

### Step 4: Evaluate the function
Since many people can share the same age (for example, all 30-year-olds), there will be multiple people \( p_1, p_2 \in P \) such that:
- \( f(p_1) = f(p_2) \)
- This indicates that the same age is assigned to different individuals.

### Step 5: Conclude the result
Since the function does not assign a unique number to each person (multiple people can have the same age), it is not a one-one function.

### Final Answer:
The function that assigns each person on Earth a number corresponding to their age is **not a one-one function**.

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