>>11365256Let V1, V2, V3, ... be an infinite sequence of vector spaces over R1, R2, R3, ... respectively. Then we define define a line as the limit L of the sequence of the span of the projection operator of v1, v2, v3,... respectively on w1, w2, w3, respectively, so long as L has only 1 basis vector. Why did I define a line as such a complicated, contrived, object?
>to provide some form of algebra-geometry interplay intuition as an alternative to set theory>to formalize OPs notion of a line>because assuming that a line is R1 is an illegal assumption. >because by saying that it is a subspace of R3 causes us to lose generality and robustness 
