2=1?

Enough with the science, here's some Maths!

a = x [true for some a's and x's]
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x]
Mindfuck.

How can this be true? What's wrong with this is that at the last stage, both sides have been divided by zero (a=x, so a-x must equal 0). This is a mathmatical impossibility. But why?

As you divide by smaller numbers, the answer gets bigger and bigger, tending towards infinity as the number you divide by tends towards 0:

10/1=10
10/0.1=100
10/0.01=1000
10/0.00001= 1000000
10/0.000000001= 10000000000
and so on:

Anything divided by zero will give infinity, and so the equation above is impossible.