Can you prove 1 equals 2?

Answer 1

Let a and b each be equal to 1. Since a and b are equal,

b^2 = ab

Since a equals itself, it is obvious that

a^2 = a^2

Subtract equation 1 from equation 2. This yields

a^2 - b^2 = a^2 - ab
We can factor both sides of the equation; a^2 - ab equals a(a - b). Likewise, a^2 - b^2 equals (a + b)(a - b). Substituting into equation 3 we get

(a + b)(a - b) = a(a - b)

So far, so good. Now divide both sides of the equation by (a - b) and we get

a + b = a
Subtract a from both sides and we get

b = 0
But we set b to 1 at the very beginning of this proof, so this means that

1 = 0

With normal algerbraic rules we know that if we add one to both sides, then both sides should still be equal, so...

1+1=0+1

2=1

Credits to the book "Zero, the biography of a dangerous idea".