Bear arithmetic

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

🧸

🧸🧸

🧸🧸🧸

Numbers

You don't have to use bears; you can also use dogs. A number means how many there are, ignoring differences.

🐶🐶🐶

Order

Numbers have an order: $1 < 2 < 3$.

But which one is "first": 🧸, 🐶, or 🐻‍❄️? Animals don't have an inherent order. We can define an order, though, for example by size.

Even and odd numbers

An even number can be divided into two equal parts; an odd number cannot, leaving a remainder of 1.

Odd	Even
🧸	🧸🧸
🧸🧸 🧸	🧸🧸 🧸🧸
🧸🧸 🧸🧸 🧸	🧸🧸 🧸🧸 🧸🧸

Definition

Let $n$ be an integer. We say:

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

Arithmetic

[show]

+	Even	Odd
Even	Even	Odd
Odd	Odd	Even

×	Even	Odd
Even	Even	Even
Odd	Even	Odd

Odd numbers have a middle

Three bears have a middle; four don't. But if three bears form a triangle, it is not clear which one is the middle. We can at least say that if an odd number of bears are lined up, there is a middle.

Prime numbers

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

Prime	Composite
🧸🧸	🧸🧸 🧸🧸
🧸🧸🧸	🧸🧸 🧸🧸 🧸🧸
🧸🧸🧸🧸🧸	🧸🧸 🧸🧸 🧸🧸 🧸🧸
🧸🧸🧸🧸🧸🧸🧸	🧸🧸🧸 🧸🧸🧸 🧸🧸🧸

#math #yuuki

Notes

[^1]: A prime number can only be rearranged into a rectangle with one side of length 1.