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?
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by
Patrick Bourg