< Math

We can think of a number $n$ as a collection of $n$ bears.

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An even number can be divided into two equal parts, while an odd number cannot.

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Definition (Even and odd numbers):
Let $n$ and $k$ be integers. We say:

• $n$ is even if there exists $k$ such that $n=2k.$
• $n$ is odd if there exists $k$ such that $n=2k+1.$

Three bears have a middle; four don't.[^1] However, if three bears form a triangle, it's not clear which is the middle.[^2] We can at least say that if a set $S$ has an odd number of elements that are arranged "in a line", then $S$ has a middle element. Such an ordering is called a linear order or a total order.[^3]

A number is composite if it can be rearranged into a rectangle; if not, it is prime.[^4] However, 1 is neither prime nor composite. The first prime numbers are 2, 3, 5, 7, 11, ....

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[^1]: Or an even number has two middles.

[^2]: Though there is a concept of the geometric median. The geometric median of the three vertices of a triangle is called the Fermat point.

[^3]: Examples of totally ordered sets: tuples ordered by index, the set of natural numbers $(\mathbb{N},\le )$, and the set of real numbers $(\mathbb{R},\le )$.

[^4]: Or a prime number can only be rearranged into a rectangle with one side 1.