The Problem With Infinity
\[x\]is an ordinary number but not when
\[x\]is infinity. This is because when
\[x\]is multiplied by 2 the result is
\[2x\]but when infinity is infinity is multiplied by infinity, the result is infinity.
Because of this following proof contains an error.
\[S=1++2+4+8+16+32+...+ \infty +...\](1)
\[2S=2+4+8+16+32+...+ \infty +...\](2)
\[S=-1\]. This is obviously wring since all terms rare positive. The above technique will only work if