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@ Daniel Wigton
2025-01-21 04:38:21
We spend too much time enthralled by even numbers. We can instantly
tell if a number is even or odd and often have preferences in the
matter. In grade school we memorize rules like
- An **even** plus an **even** is an **even**
- An **odd** plus an **odd** is an **even**
- An **even** plus an **odd** is and **odd**
And so forth to rules of multiplication. But this magical quality of
numbers really just means *evenly divisible by 2.* What is so special
about 2? Shouldn't we just as well care if a number is divisible by 3?
So I am introducing **threeven numbers** as all numbers divisible by
3.
0, 3, 6, 9, 12, 15, ...
are all threeven numbers. But what about numbers that aren't divisible
by 3? Numbers that are not divisible 2 are called *odd* so I guess
*throdd?*
There is, however, a slight problem. There seem to be more throdd
numbers than threeven numbers.
1, 2, 4, 5, 7, 8, 10, 11, 13, 14, ...
To solve that we need to think about what an odd number is. If an even
number is some number *n times 2* or *2n* then odd numbers are *2n +
1*
This gives a nice way to think about threeven numbers as well. Every
threeven is *3n* and a throdd is *3n + 1* and we need to introduce
throdder numbers as *3n + 2*. There isn't any reason that there should
only be two types of numbers. So instead of numbers that are divisible
by 2 and numbers that aren't, we have numbers that are divisible by 3,
numbers that are 1 greater than a multiple of three and numbers that
are 2 greater than a multiple of three.
To recap
- Threeven = *3n*
- Throdd = *3n + 1*
- Throdder = *3n + 2*
Now for handy rules of thumb.
- A **threeven** plus a **threeven** is a **threeven**
- A **threeven** plus a **throdd** is a **throdd**
- A **threeven** plus a **throdder** is a **throdder**
- A **throdd** plus a **throdd** is a **throdder**
- A **throdd** plus a **throdder** is a **threeven**
- A **throdder** plus a **throdder** is a **throdd**
And, for multiplication
- A **threeven** times a **threeven** is a **threeven**
- A **threeven** times a **throdd** is a **threeven**
- A **threeven** times a **throdder** is a **threeven**
- A **throdd** times a **throdd** is a **throdd**
- A **throdd** times a **throdder** is a **throdder**
- A **throdder** times a **throdder** is a **throdd**
This is just modular arithmetic and the same can be done for any integer *n*
*m mod n = 0*
Means *m* is an **nven** and there will be *n - 1* varieties of **nodd**
**Threeven**, however, is the most fun to say and makes the point nicely, there is no need to carry it further.
Note: it appears that I am not the first to have discovered threeven
numbers. And now you are stuck knowing about them as well.