u/Next-Ad4782

Hello,

I just finished the season 2 ending and I noticed an issue for which i can't find a good answer for, except that || In the randomness of an large number of universes, she somehow didn't do it or she just copied the data ||.

The issue is that || Our Maddie (let's say layer L) after becoming god, takes over the Maddie in an universe "lower" than hers (let's say L+1). Now, if you remember before, it was shown that the exact events which happened to our Maddie was being guided by a Maddie in an universe "above" hers (let's say L-1) (We see David come and the exact same scene of Maddie letting Pope release safe surf). Now, if our Maddie (L) was taken over, then this creates a number of issues:

1. Maddie (L) wasn't taken over -> The Maddie above (L-1) just didn't do it for some reason after coming so far (maybe it wasn't exactly what she wanted, I don't like this answer a whole lot, especially because I think the outcome is being guided towards a predetermined state by a safe surf way higher in the ancestral chain of universes (atleast <L-1).
2. The other answer is that Maddie (L-1) puts back the (L layer) Maddie and also, did a reset of state, wherein Dave/Caspian/David remain dead.

2nd seems more plausible but opens up another question wherein our (L) Maddie could have somehow breached to L-1 layer and performed time travel through a rollback of memory state .. LOL ||

I recently saw a proof regarding

$$ \sqrt{i} = \pm \frac{1+i}{\sqrt{2}} $$

This was shown by solving the equations obtained from

$$ (\sqrt{i})^2 = (a+bi)^2 $$

I understand the algebraic steps, but I’m confused about the logic behind why this is valid.

From my understanding, this seems to suggest that two complex numbers (x) and (y) can be equal whenever

$$ f(x)=f(y) $$

for the function

$$ f(x)=x^2 $$

But then I can also show that both (\sqrt{i}) and (-\sqrt{i}) satisfy the same equation, which seems to imply

$$ \sqrt{i}=-\sqrt{i} $$

and therefore

$$ \sqrt{i}=0 $$

Clearly something is wrong with my reasoning, and I’d like to understand exactly where the mistake is.

Is the original derivation actually valid? If so, what rule am I misunderstanding?

I think (\sqrt{i}) not being a complex number in the usual form (a+bi) might be the issue.