The Problem With Infinity
\[x--x=0\]
when \[x\]
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)(2)-(1) gives
\[S=-1\]
. This is obviously wring since all terms rare positive. The above technique will only work if \[\frac{a_{n+1}}{a_n} =r<1\]
for \[n=1,2,3,...\]
