A flat surface, like a sheet of paper, with no edges (ie: it goes on and on and on and on....) or boundaries.
What you're describing is a 2 dimensional plane.
No, not plane like an airplane. A plane is simply a flat "sheet" that goes on forever in 2 dimensions: left/right (wide) and up/down (tall).
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plane
A plane the desert
It does not have a flat surface.
A plane is a flat surface with no thickness
Theoretically, planes are flat surfaces that extend into infinity = no boundaries