0 = 1 - 1 + 2 - 2 + 3 - 3 + 4 - 4 L1
The above is fine, but what about the infinite version:
0 = 1 - 1 + 2 - 2 + 3 - 3 + 4 - 4 + ... L2
There is nothing wrong with writing out infinitely many terms like this.
Yet we can re-arrange it to give
0 = 1 + ( -1 + 2 ) + ( -2 + 3 ) + ( -3 + 4 ) + ( -4 + 5 ) + ... L3
= 1 + 1 + 1 + 1 + ...
= infinity