Octonion numbers are a special type of number system that extends the idea of real numbers, complex numbers, and quaternion numbers. Just like how you learned about counting with whole numbers, then learned about adding and subtracting with negative numbers, octonion numbers are like a new level of numbers that we can use to do even more advanced math.
Let's start with what you already know: real numbers. Real numbers are the ones you've been using for all your math so far - numbers like 2, -5, 0, and 3.14159. Then you learned about complex numbers, which have a special number called 'i' where i^2 = -1. For example, 3 + 2i is a complex number.
Quaternions are the next level. They're like a special type of complex number with three extra 'imaginary' numbers: i, j, and k. Just like how we can add, subtract, multiply, and divide real and complex numbers, we can do the same with quaternions.
Now, octonion numbers take it one step further. They have even more 'imaginary' numbers, which means they can do even more complex math. But these numbers are really tricky and don't follow all the same rules as the numbers you've learned before. For example, when we multiply octonion numbers, the order matters, just like when we multiply matrices.
So, think of octonion numbers as a really cool and advanced type of number system that people use in very complex math and physics. It's like learning about new tools in a toolbox that mathematicians and scientists use to solve big, hard problems.