How do I notate that $1/2$ children do not exist

Question

Suppose that,

• the average person has $2$ $1/2$ children.
• only whole children exist

It should be straightforward to notate:

• If an average person exists, then that person has two $1/2$ children
• there does not exist $1/2$ a child
• Therefore, the average person does not exist.

However, I can't figure out to notate the $1/2$ child part so that the meaning of $1/2$ is clear. The problem, as I see it is that if whole children exist $(1/1)$ then half children exist $(1/2 + 1/2)$.

How do I convey the idea in notation?

Answer 1

I would say it like this: "Statistically a person has on average a half child." It is different from your wording. An average person cannot have a half child.

Mathematical formulation:

$x_i:$Number of children of person i

$x_i \in \mathbb N$

$\overline x:$ Average number of children per person.