Let’s prove that \(1=2\). Take a number \(a\) and suppose \(b=a\). After multiplying both sides we have \(a^2=ab\). Subtract \(b^2\) from both sides to get \(a^2-b^2=ab-b^2\). The left hand side is a difference of two squares so \((a-b)(a+b)=b(a-b)\). We can cancel out \(a-b\) and obtain that \(a+b=b\). But remember from the start that \(a=b\), so substituting \(a\) for \(b\) we see that \(2b=b\), dividing by \(b\) we see that \(2=1\).