Quote Originally Posted by Jack_Simth View Post
As you've paraphrased that, it is a fallacy, and is going in the opposite direction of what I went over.

Your paraphrase is starting from a finite number of items in an infinite space - which means a density that is indistinguishable from 0.
I'm starting with pointing out that we've got a definition that says the density is nonzero in this infinite space.

Your paraphrase is saying that the extreme rarity means that what you see is impossible (which is not the case - if there are five of something, then there are five of something, and encountering one of them simply requires going to where it is - completely irrespective of the volume it might be spread over).
I'm pointing out that the nonzero density in an infinite space means that there's an infinite number of the thing I'm looking for.

The D&D planar cosmology includes such things as Subjective Directional Gravity and Erratic Time. D&D, very explicitly, includes things that are not real things and have severe issues if we try them within the confines of physics as we know them in the real world. That doesn't make it any less applicable to the game.
You are going in the opposite direction, but using the same logic. you are saying if you do meet somebody in an infinite space, there must be an infinite number of them, because otherwise the chance of meeting them would be zero.

This is not rational in the real world, and it isn't rational in a fantasy world. You are trying to apply abstract math to a setting which runs off of belief (in character) and game play and narrative mechanisms (out of character).

Encounter tables are not, nor have they ever been, intended to be an accurate sampling of the population of a given area, let alone an infinite area.