# Set Theory

• September 11th 2008, 07:34 AM
Set Theory
Let L denote the set of straight lines through the origin in $\mathbb{R}^2$. Let M denote the set of straight lines through (1,1) in $\mathbb{R}^2$. How many elements does $L \cap M$ 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)?
• September 11th 2008, 07:42 AM
Plato
How many points are needed to determine a unique line?
How many lines in L pass thru (1,1)?
• September 11th 2008, 08:10 AM
bkarpuz
Quote:

Let L denote the set of straight lines through the origin in $\mathbb{R}^2$. Let M denote the set of straight lines through (1,1) in $\mathbb{R}^2$. How many elements does $L \cap M$ have?
only $1$.
because there is only one line passing through $(0,0)$ and $(1,1)$.
Lagrange's theorem. From $n+1$ different points on $\mathbb{R}^{2}$, there is only one polynomial of $n^{th}$ order which passes from all of these points.