UNNERVED

Ready for a little maths?

Alright. Let's start with x = y. That means that whatever value you give x, y is going to be exactly the same thing.

If x = y, then squaring x is no different to multiplying x by y.

x² = xy

So far, the universe is with us, so let's start playing around with the equation. You remember, that in order for both sides of an equation to balance, whatever you do (dividing, multiplying, adding, etc), you have to do, equally, to both sides: like a see-saw. So let's take off the same value from left and right: let's subtract y².

x² - y² = xy - y²

We can do something nifty here. Algebra helps us out. First of all (look at the left hand side):

x² - y² = (x+y)(x-y)

You know this because multiplying out the brackets gives you x² + xy - xy - y², and the two bits in the middle add up to 0: x² - y².

So.. that means:

(x+y)(x-y) = xy - y²

But there's also a y in both bits of the right hand side we can factor out: xy - y² = y(x-y).

(x+y)(x-y) = y(x-y)

Looking at the see-saw, there's probably something else we can do now. Both sides have an (x-y) factor, so we can divide both the left and right by (x-y) and they'll disappear:

(x+y)(x-y) = y(x-y)

(x+y) = y

x+y = y

We started with x = y, so it must also be true that:

x+x = x

2x = x

2 = 1

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And that's a pretty good description of how I'm feeling today. Unnerved, but not quite sure why, as though the space-time continuum might have doubled (or halved) in size and nobody's noticed. As though 2+2 is now equal to 2 or maybe 3, or (crazily, I know) 4!

I'm sure it'll be fine. It'll be fine, right?

It'll be fine.