I know that if
for values of $x$ where the infinite power tower converges, so when $x\le e^\frac1e$. However, when I put the power tower into Desmos, it seems to stop being accurate at around $x\approx0.1$, no matter how many $x$'s I add.
If it is truly infinite, is it accurate all the way to 0, or does it stop? How can it be proven either way?