I wanna add to what other users already answered that this problem is not created by federation, only exacerbated.
If I’m mod of a community and I ban your Lost_My_Mind@lemmy.world account, I cannot stop you from creating, e.g. Lost_My_M1nd@lemmy.world and coming back. Most servers have some barriers against spam account creation in place, but I’d wager you could easily create a handful of accounts on a server until they start to grip.
Even completely centralized platforms such as Twitter and Reddit are the same. You can easily ban/block evade a couple times per timeframe.
Sorta. The function height(angle) needs to be continuous. From there it’s pretty clear why it works if you know the mean value theorem.