Question

What is an example of a bad mathematical proof?

Answer 1

Another bad proof is:

Prove that 2=1

\begin{aligned}
&-2=-2 \\
\Longrightarrow & 4-6=1-3 \\
\Longrightarrow & 4-6+\frac{9}{4}=1-3+\frac{9}{4} \\
\Longrightarrow &\left(2-\frac{3}{2}\right)^{2}=\left(1-\frac{3}{2}\right)^{2} \\
\Longrightarrow & 2-\frac{3}{2}=1-\frac{3}{2} \\
\Longrightarrow & 2=1 .
\end{aligned}

Answer 2

An example of a bad proof is :

Prove that 1=2

\begin{aligned}
& a=b \\
\Longrightarrow & a^{2}=a b \\
\Longrightarrow & a^{2}+a^{2}=a^{2}+a b \\
\Longrightarrow & 2 a^{2}=a^{2}+a b \\
\Longrightarrow & 2 a^{2}-2 a b=a^{2}+a b-2 a b \\
\Longrightarrow & 2 a^{2}-2 a b=a^{2}-a b \\
\Longrightarrow & 2\left(a^{2}-a b\right)=a^{2}-a b \\
\Longrightarrow & 2=1 .
\end{aligned}