Calculus Level 4

In which step did we first make a mistake?

$\begin{array} { l l l } 0 & = \displaystyle \sum_{i=0}^\infty 0 & (1) \\ & = \displaystyle \sum_{ i=0}^ \infty (1 -1) & (2) \\ & =\displaystyle \sum_{ i=0}^ \infty 1 - \displaystyle \sum_{i=0}^\infty 1 & (3) \\ & = \left ( 1 + \displaystyle \sum_{ {\color{red}i=1}}^ \infty 1\right) - \displaystyle \sum_{j=0}^\infty 1 & (4) \\ & = 1 +\displaystyle \sum_{ j=0}^ \infty 1 - \displaystyle \sum_{j=0}^\infty 1 & (5) \\ & = 1 +\displaystyle \sum_{ j=0}^ \infty (1 - 1) & (6) \\ & = 1 & (7) \\ \end{array}$

×