Yes, except for the assumption that 1-1+1-1+1-1+1-... = 0.5 or 1/2. "Because we don't know whether to stop after a +1 or after a -1, we just average the two possible answers," is just a completely arbitrary solution. The little three dots, indicating that the equation goes on forever, mean that the equation must be conceptual only, because one must NEVER STOP calculating it. The idea that we must pick either a +1 or a -1 to stop at ruins the whole thing. Then arbitrarily deciding just to average the two possible answers ruins it again. It's ruined squared.
And 1+2+3+4+5+6+... is also conceptual only for the same reason. It cannot actually have any concrete answer, much less -1/12. So they can write proofs until the cows come home, but it's all meaningless. In fact they hint at this themselves without ever realizing it. They point out that in physics, we can not actually deal with infinite measurements. Well no duh. The same applies to these conceptual equations. We cannot actually answer them. The whole premise that we can assign a finite answer to a never-ending calculation is flawed right out of the gate.
The only examples of never-ending equations that can be answered are ones that could be restated as equations that end. Such as 1*1*1*1*1*... because obviously its value is the same as 1*1. Continuing to carry out additional operators never changes the value. Or 0+0+0+0+0+... has the same property.
