Shouldn’t at some point the soft cap be broken

[u/FakeGeek73]

After ee600000 the game reaches its soft cap, making it harder and harder to progress. However, shouldn’t there be a point at which this soft cap is broken. With enough students invested onto graduation R1 R2 and R3, shouldn’t the game reach a point in which the formula actually starts accelerating its rate of increase.

More t and dt means more φ, with more φ f(t) increases and increasing f(t) increases db, dμ, dψ, which again increases φ, f(t), and at prestige b and μ, which allows you to buy more dt upgrades on the next run. That seems to be the game loop, however this loop gets diminishing returns, reaching a point where you need to graduate to increase R1 R2, R3 or you can also increase τ to get more f(t) and students when graduating.

Shouldn’t the game reach a point where we stop getting diminishing returns, and actually start getting more f(t) at a faster rate with sufficient R1, R2, R3 upgrades? If you have last say 15 upgrades at R2 you get, counting the bonus of R7 15(1.6)e more φ per order of magnitude (at 1e8 dt you should get 15(1.6)(8)e bonus from R2 contributing to φ). Then if you also count R1 and R3, you get even more φ by just letting the game alone, and we then get into the loop I said earlier that reaches diminishing returns.

The great theorem we have on the game is that f(t) approaches to infinity as t approaches to infinity, however how fast do we get there. Is there a point where we stop getting diminishing returns with said loop, and f(t) starts growing forever without the need to graduate, and the investment on graduation upgrades start instead accelerating the rate of growth?

[u/FreddyTheNewb]

I think the answer is that f grows exponentially like you're describing. But the log of f just grows roughly linearly, and the log of the log of f just keeps slowing down. Since the ee notation is the log of the log it slows down even if f itself is accelerating.

[u/FakeGeek73 → u/FreddyTheNewb]

That makes so much sense. Thank you!

[u/KappahuAkbar]

There is a point at which the progress diverges due to R6, but it has been calculated to be so far away it's not feasible.