Um, how exactly is the mathematical system different to the normal mathematical system? As far as I recall, 2 follows 1, and 3 follows 2, etc etc. And 2 > 1, therefore there is ordinality. Hence, if I drew 7 Ultima, and then the next time, I drew 5 Ultimas, I drew 2 less Ultimas. The first time meant I could cast it 7 times, the second 5, and the difference was -2. All of these numbers have a significant meaning. Therefore, there is a cardinal number system. The moment you have a cardinal number system, most (if not all) mathematical laws hold (like addition, subtraction, multiplication, logs, antilogs, calculus).
So, mathematics is definitely very close, if not identical to our mathematics.
Okay. A sorceress has a normal human lifespan. Rinoa is a sorceress. Therefore, Rinoa has a normal lifespan. The maximum of a normal lifespan is realistically 100. Therefore Rinoa's life constraint is:
X+Y <= 100 (where X is how long she has lived, and Y is the amount of years she will live in the future).
X = 17 (read the game manual).
Therefore Y <= 83.
The distance between the beginning of the game and Ultimecia's time is
Z = B - A, where Z is the distance, B the year of Ultimecia and A the year of the beginning of the game.
Ultimecia lives many generations in the future. A generation is generally considered 30 years. So Z >= 30M, where M is how you define many. Personally, I'd say 10 is many, although from the most minimal point of view, 5 would do.
Therefore, Z >= 30 x 5
Z >= 150
But for Rinoa to be Ultimecia, she must be able to at least live until Ultimecia's time, i.e. Y > Z.
But the maximum of Y is 113 and the minimum of Z is 150, and therefore Y > Z can never hold.
Therefore Rinoa <> Ultimecia (sorry, no unequal sign available).
No, in this case it is important to point out that the alternative timeline cannot exist, because it is not possible. How does my post come from speculation? Please highlight the speculative elements of my post. And mathematics is not random.
Actually, as far as I'm aware, there aren't any methods to get into a timeline that infinitely loops. If you could, it would badly mess up with the circle of events, and would mess up the loop and quite possibly tear open the fabric of space and time. But the loop that we play through seems quite perfect, and the fabric of time & space is still intact. But if you have any theories on how to get into a certain timeline, please let us all know.
R<>U is not fundamentally flawed. I just proved it above. R=U is fundamentally flawed, as I proved previously. Therefore, something that is fundamentally flawed cannot be considered at all when the alternative is fundamentally flawless.
I concur.





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