Fun With Math-Superpowerition: Inventing a Super Power Operation -- Introduction

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Introduction

In the beginning of time, there were once small groups of similar items spaced far apart. Each of the small groups were once islands of their own. Some numbered as few as one or as many as 1,000,000, but many groups were of much more managable small numbers.

Let's say we're looking at two groups of apples. One group has two. Another group has three. Nobody ever thought of combining the two groups into one bigger group for a while until someone invented the idea of adding the one group with two to another group with three.

2 + 3 = 5

The result is a group of five apples, thus, the addition operation was born, represented with a "+" sign.

Later on, someone had the idea of taking a pair of apples, putting it on a table, then taking another pair of apples and putting it on the same table, then taking yet another pair of apples and putting it on the same table. We now have three groups of two apples. Someone added them together the hard way:

2 + 2 + 2 = 6

Since we're adding three groups of two's, why not simplify the operation by simply multiplying two by itself three times.

2 × 3 = 6

Either way, the result is six apples, thus, the multiplication operation was born, represented with a "×" sign.

Things were well until one day some wacky calculus engineer or whoever decided to multiply the number two three times like this:

2 × 2 × 2 = 8

By accident, or planning, yet a new operation would be born by simplifying the operation into this:

2 ^ 3

or to be more compact:

2³

And that's how the exponentiation operation was born. If it weren't for the exponentiation or multiplication operations, you would be stuck with addition, and the answer of the number eight would be gotten by adding two more apples to the original two to get four, then adding four more apples to that four to get eight.

2 + 2 = 4, then, (2 + 2) + (2 + 2) = (2 + 2) + 4 = 4 + 4 = 8, or to break it down, 2 + 2 + 2 + 2 = 8.

Let's try this with three cubed. You could use exponentiation like this:

3³

Or multiplication:

3 × 3 × 3

Or addition:

Start with 3, then add three copies of itself together, then add three copies of the sum of the three copies of itself together:

(3 + 3 + 3) + (3 + 3 + 3) + (3 + 3 + 3)

Complicated, isn't it.

But wait, there's more!

Let's say we have the number two raised to itself like this:

2²

Now let's raise the figure above by the original number like this:

(2²)^² or simply (2 ^ 2) ^ 2

Note that you can use the Unicode uparrow symbol (↑) in place of the caret, but for most purposes, you'll see a caret.

That is, we're raising two to the power of itself twice. Note that we're going from left-to-right or down-to-up.

So is there a mathematical operation to simplify it? Not that I know of, however, there could be a use for it in some field sometime down the line. I need to get a notation representative for the Superpowerition (Super Power) mathematical operation. Since it is a super operation combining addition with multiplication and exponentiation, I'll use this Unicode symbol I found below for the notation:

✱

This is not to be confused with the asterisk that is often used in coding for multiplying two numbers.

Superpowerition is represented using either the decimal code ✱ or the hexadecimal code ✱

So to represent (2²)^² or simply (2 ^ 2) ^ 2, you can use this:

2 ✱ 3 = 16

This raises the number two to the power of itself and the result of that is raised to the power of the original number (2 ^ 2) ^ 2, hence the "3" means that there are three copies of the number "2" in this operation.

When you exponent "2" to the power of "3", you're multiplying "2" by itself and the result is multiplied by the original number ((2 × 2) × 2).

So to sum up the four mathematical operations:

2 + 3 = 5

2 × 3 = 6 (2 + 2 + 2)

2³ = 8 (2 * 2 * 2) or ((2 + 2) + (2 + 2))

2 ✱ 3 = 16 (2²)^² or simply (2 ^ 2) ^ 2 or ((2 × 2) × (2 × 2)) or ((2 + 2) + (2 + 2) + (2 + 2) + (2 + 2))

Introduction

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