When comparing the actual height of a mountain, they're measured from their base (which is whatever elevation the ground they sit on is) to their peak, rather than just looking at their peak altitude. This is how you compare mountains on other planets, and why Mons Olympus on Mars is the tallest mountain in the solar system. For Mauna Kea, the mountain is taller than it looks because its base sits at the bottom of the ocean, whereas Everest sits on an already-lofty piece of continental plate.
I get the impression that the asker knows that but that their question is more like, is there any official way to define where the mountain starts? Could we keep tracking the side of Everest right down into a far-off ocean trench and say it's now the tallest again, it's just also really wide?
I guess you're looking for obvious local minima. If the land slopes back up a lot or stays mostly flat for a long time it's probably not part of the mountain anymore. Would a smaller mountain in the middle of Uluru be measured starting from ground level at the top of Uluru?
Edit: Asker has now confirmed in a separate comment that this is what they meant.
My definition would involve some definition of geological homogeny such that you could classify the terrain as mountain and not-mountain. Probably based on whether it was involved in the process that formed the mountain.
Yeah, that was what I was hoping/expecting the definition would use, that mountains come from some plate interaction involving lava which would provide a natural boundary between "mountain" and "rest of earth".
I think a lot of mountains don't involve lava at all, they're just the product of continental plates running into each other. I'm pretty sure Everest is an example of this. Hawaii is the opposite; those mountains don't involve plates at all, they're solely the product of lava.
Why is "height from the solid matter base" more correct than "height from the non-gaseous matter base" though. From the perspective of humans, who generally live at the border of gaseous matter not the border of solid matter, I think the latter might make more sense.
