Even conventional mathematics allows that we might start with different definitions and assumptions, which in plain English might appear to contradict one another. Mathematics has no problem separating these alternatives into separate “namespaces”.

We’re allowed to use the same key words (e.g. “basis vector”) differently. Contradictions get defined away, but to the layman the variants may still seem “at odds”.

In Quadray Coordinates (see Wikipedia) four “basis vectors” emanate from the origin (0,0,0,0) to the four corners of a regular tetrahedron (1,0,0,0) (0,1,0,0) (0,0,1,0) (0,0,0,1). None are said to be linearly dependent on the others as rotation is not required for space spanning, only a grow-shrink operation (positive scaling) and conventional vector addition.

Is this a contradiction of XYZ? Even if we conclude space is therefore 4D?

Not if we’re willing to allow for these different definitions.

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