on top of that, 'e' is the only base b such that d/dx b^x = b^x. every other base induces some multiplicative factor in the derivative, hence why it's considered the 'natural' base for exponentials and logarithms.
green_pyroxene
joined 2 years ago
well, TJ "Henry" Yoshi, hear me out. an instance of Losing the Game actually has three parts to it: when you start thinking about the Game, when you are thinking about it, and when you stop thinking about it. and together, this forms one complete Game Loss. now usually, it's when you start thinking that's important, because that's the only part that increases your Loss counter. however, sometimes it's sufficient to keep thinking about it continuously, which allows the player to decide to announce their Loss and make people around them Lose as well. what this implies is that, in the context of a full Game run, any instance where you declare having Lost the Game can "leech off" of a previous Game Loss, which keeps the total count of complete Losses the same. so in conclusion, since that Loss counts in some contexts, but adds no additional Losses in other contexts, we refer to it as a half Game Loss.
"it doesn't need to go over the horizon to disappear in the distance", but the problem is that it does go over the horizon rather than disappearing, as anyone who's seen a sunset can attest