Are terms like "2D point", "3D line" legal?

Question

Dimension says:

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it.

Dimension (vector space) says:

In mathematics, the dimension of a vector space $V$ is the cardinality (i.e. the number of vectors) of a basis of $V$ over its base field.

Now my question is: Is using terms like $2D\ point$ or $3D\ line$ legal? I think using those can cause mistakes and doubtful during thinking and solving problems.

Answer 1

The terms "2D Point", "3D Point", "2D Line", "3D Line", "2D Surface", "3D Surface" etc... are all acceptable in conversation. Typically, these terms are clearly referring the dimension of the space containing the line, point, or surface, so as long as the appropriate context is provided, I would say these terms are "legal".

But, in my opinion these terms should be avoided in formal documents such as journal papers, conference papers, research articles, etc... It is certainly more precise to say "point in two-dimensional space", "surface in three-dimensional space", etc...

Answer 2

Yes, saying "2-D point" and "3-D line" are perfectly okay. For example, $(2, 5)$ is a so-called "2-D point." Lines also exist in 3 dimensional space. However, in a formal mathematical paper, one should not use the terms "2-D point" and "3-D line", since they are ambiguous.