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Math Help - Set Theory

  1. #1
    Super Member Deadstar's Avatar
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    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)?
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  2. #2
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    How many points are needed to determine a unique line?
    How many lines in L pass thru (1,1)?
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  3. #3
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by Deadstar View Post
    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)?
    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.

    Sorry for my poor English. :$
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