We can think of a positive integer $n$ as a set of $n$ blocks arranged in a line--the same as marbles, dominoes, or any other countable objects.

Integers from 1 to 10:

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

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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. However, if three doors form a triangle, we may not know which one is the middle. If a set $S$ has an odd number of elements arranged in a line, then $S$ has a middle element. It seems that such an ordering is said to be a linear order (or total order).