We can think of a number $n$ as a collection of $n$ blocks (or marbles, dominoes, or any other countable objects).

Numbers from 1 to 10:

o

oo

ooo

oooo

ooooo

oooooo

ooooooo

oooooooo

ooooooooo

oooooooooo

An even number can be divided into two equal parts, while an odd number cannot. Halving an odd number leaves a remainder of 1.

o

o
o

oo
o

oo
oo

ooo
oo

ooo
ooo

oooo
ooo

oooo
oooo

ooooo
oooo

ooooo
ooooo

Definition (Even and odd numbers): Let $n$ and $k$ be integers. We say that $n$ is even if there exists $k$ such that $n=2k$, and $n$ is odd if there exists $k$ such that $n=2k+1$.

Three doors have a middle one; four don't.[^1] However, if three doors form a triangle, it may not be 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. It seems that such an ordering is called a linear order or total order.[^3]

[^1]: One can also think of an even number as having two things in the middle.

[^2]: It seems there is a concept called 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 $(\mathbb{R},\le )$.