Results 1 to 3 of 3

Thread: Set Theory

  1. #1
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722

    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)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,737
    Thanks
    2812
    Awards
    1
    How many points are needed to determine a unique line?
    How many lines in L pass thru (1,1)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member bkarpuz's Avatar
    Joined
    Sep 2008
    From
    R
    Posts
    481
    Thanks
    2
    Quote Originally Posted by Deadstar View Post
    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. :$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Jul 8th 2011, 06:09 PM
  2. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  3. Problems relating Theory of Automata (Computer Theory)
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: Oct 17th 2007, 09:52 AM
  4. Set theORY
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2007, 07:01 PM
  5. Set Theory
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Feb 27th 2007, 09:22 AM

Search Tags


/mathhelpforum @mathhelpforum