Question

Suppose x = 1

Then x2 = x
x2 - 1 = x - 1
(x - 1)(x + 1) = x - 1
(x + 1) = 1
x = 0
So 1 = 0.
Is this possible? What led to this ridiculous conclusion?

Answer 1

No! Never divide by 0!

Explanation:

Ah, the famous 1 = 0 proof.

There is just one error: you can never divide by 0!

We're starting off by assuming x = 1, but in this step:

(x - 1)(x + 1) = x - 1

(x + 1) = 1

we end up dividing by x - 1, which equals 1 - 1 = 0.

Whenever you start dividing by zero, funny business starts happening. This isn't possible.