# Thread: Set Theory

1. ## Set Theory

Let L denote the set of straight lines through the origin in $\displaystyle \mathbb{R}^2$. Let M denote the set of straight lines through (1,1) in $\displaystyle \mathbb{R}^2$. How many elements does $\displaystyle L \cap M$ have?

Is this just how many times the lines intersect? If so is it not just LxM intersections including the origin and (1,1), or, (LxM)-2 not including the origin of (1,1)?

2. How many points are needed to determine a unique line?
How many lines in L pass thru (1,1)?

3. Originally Posted by Deadstar
Let L denote the set of straight lines through the origin in $\displaystyle \mathbb{R}^2$. Let M denote the set of straight lines through (1,1) in $\displaystyle \mathbb{R}^2$. How many elements does $\displaystyle L \cap M$ have?

Is this just how many times the lines intersect? If so is it not just LxM intersections including the origin and (1,1), or, (LxM)-2 not including the origin of (1,1)?
only $\displaystyle 1$.
because there is only one line passing through $\displaystyle (0,0)$ and $\displaystyle (1,1)$.

Lagrange's theorem. From $\displaystyle n+1$ different points on $\displaystyle \mathbb{R}^{2}$, there is only one polynomial of $\displaystyle n^{th}$ order which passes from all of these points.

Sorry for my poor English. :\$