Affine Set

https://www.youtube.com/playlist?list=PLz7t89zv8Lp2zZccWisU4ZDfs2eXtSN71

Let $F^n$ be the vector space. The a flat (affine set) is a subset of $F^n$ which is congruent to $F^m$ for some 0 ⇐ m ⇐ n.

In following example, the vector space is $\mathbb{R}2$ i.e. the set of all 2 dimensional vectors. so n = 2
The blue line, is $\mathbb{R}1$ i.e. set of all real numbers (the line represents a real number line)
The blue line is congruent to the X axis (or Y axis too). So the blue line is a valid affine set.

This can be extended to 3D vector spaces also.