Everyone all right? Hmmm... that rabbit hole wasn't that bad, was it?

Anyway, welcome to Mathsland. On behalf of Mathsland, I wish every one of you a happy journey ahead.

This is the field of Algebra. We'll start by taking in the scenery... hello, there's x. Hey, x, come over here!

Oh, hi, Alice. How do you do? Oh, and YOU! I heard Alice was about to bring new people here, but I didn't expect it to be so fast. How do YOU do? Pleased to meet you.

Now, x, do stop your chatter and get our friend acquainted with the field of Algebra.

Sure, Alice. Greetings again to you! I am but an ordinary citizen of Algebra - But the most useful one - On the contrary, Alice. I think I'm too popular for my liking. Anyway, I am the symbol you'll encounter most frequently in your journey here. I might as well be Alice's deputy guide, if she doesn't mind? Thank you, Alice, you're so kind.

Well, anyway, some people may tell you that I am a number. This is certainly FALSE. I am a variable, and I represent any number, but depending on the equation I happen to be in, I will represent certain number(s). Since I have to represent numbers, therefore, I have properties similar to numbers, for example, bring another me and you get 2 of x, or 2x. Drag another fellow in, and divide us into 3 groups, then 3x/3 will give you x, one of me in each group.

You want power? Sure, of course. It's simple. If I get x number of me, and add us up, you'll get xx, or x², just as if you multiply 2 by 2 to get 2² or 4.

So, you see, we represent numbers, but we are not numbers. If we were numbers, I will only be one number at any one time, but I can be two, three, or more.
You're interested in who 'we' are? Sure, come along. Let's take a tour of our residences.
...
Here's my humble house. You'll find my neighbours are all the letters you know, 'a', 'b', 'c',... up to 'y' and 'z'. 'Y' is my neighbour, and a useful fellow also. 'A', 'b' and 'c' are in that triangular plot there. 'Z' is below us; he likes depth. But we must move on...
Here's the Greek pasture. 'Tis the home of the Greek letters... oh, beg your pardon, you don't know Greek. Well, that won't be a trouble. You don't need to know them all. There's alpha, over there, and beta at his side. Gamma is nearby, but I don't see him long enough in one place. Oh, and pi, of course. She's a symbol, yes, but she usually acts as a constant. You can see her now with her long train behind her... there, the damsel starting with 3.14159265354......

x, why don't we go to the playgrond?

The playground? Whatever for, my dear?

x, don't you remember? The Equator! It's fun!

Oh, the Equator. Well, fine with me. It'll be just splendid too, for our visitor. Come along!

Ah! here we are. Now, if you don't mind, I'll get my friends over here. Hey! Come over here! Alice is here, and she wants to play!
Well, they're here now, all the x's that I can call for. You want to play that game again?

Yes!

All right, Alice on this side, x's on the other. Hmmmm... what do we have here?

Right, now given Alice's weight is 42kg - you are, aren't you? - what is x?

Correct, 6. x represents 6. Or rather, x=6. Here, now, what do we have here?

This messes up a bit, but never mind. Observe. 2, shift to Alice's place. Now, the Equator makes sure all of us switch signs when we shift. So now it is as such.

Now, Alice's weight is 42, so what is x? Yes, x=8 now.