# How can 1 = 0 ?

**Logic**Level 2

{1} Suppose that \(x\) satisfies : \(x-1 = 0\).

{2} But then that \( \implies (x-1)(x-2) = 0\)

{3} which implies \( x-1=0 \quad \text{ or } \quad x-2 = 0\)

{4} which implies \( x=1 \quad \text{ or } \quad x=2\)

{5} So, in particular, \(x=2\) is a solution to the first equation and hence, by substituting in, we obtain : \[1=0\]

Can you tell poor Peter where his argument goes wrong?