Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By HallsofIvy
  • 1 Post By Plato

Thread: Real Number Line and xy-Plane

  1. #1
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Real Number Line and xy-Plane

    The real number line includes negative numbers, 0, and positive numbers. I also know that the x-axis and y-axis include the same. It is logical to say that the x-axis and y-axis are both real number lines that meet at the origin?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    20,239
    Thanks
    3355

    Re: Real Number Line and xy-Plane

    Yes, that is true. Even more, they form four right angles where they intersect and "right angles", or angles in general, cannot be defined in only one dimension. A Cartesian coordinate system, with x and y axes, can only be constructed in $\displaystyle R^2$ which is two dimensional.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Real Number Line and xy-Plane

    Quote Originally Posted by HallsofIvy View Post
    Yes, that is true. Even more, they form four right angles where they intersect and "right angles", or angles in general, cannot be defined in only one dimension. A Cartesian coordinate system, with x and y axes, can only be constructed in $\displaystyle R^2$ which is two dimensional.
    If R^2 = two dimensions, can we say that R^3 = three dimensions involving a third variable?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,348
    Thanks
    3243
    Awards
    1

    Re: Real Number Line and xy-Plane

    Quote Originally Posted by harpazo View Post
    If R^2 = two dimensions, can we say that R^3 = three dimensions involving a third variable?
    Yes indeed.
    $\mathbb{R}^1$ is the set of real numbers.
    $\mathbb{R}^2$ is the set of pairs of real numbers.
    $\mathbb{R}^3$ is the set of triples of real numbers.
    Thanks from harpazo
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Real Number Line and xy-Plane

    Quote Originally Posted by Plato View Post
    Yes indeed.
    $\mathbb{R}^1$ is the set of real numbers.
    $\mathbb{R}^2$ is the set of pairs of real numbers.
    $\mathbb{R}^3$ is the set of triples of real numbers.
    Good to know in advanced. I plan to study Calculus 3 in the future. I always wanted to complete the calculus series.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Aug 30th 2012, 12:56 PM
  2. interval on real number line
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jan 28th 2010, 05:26 PM
  3. Infinity and the Real Number Line
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Jan 21st 2010, 02:26 PM
  4. Proof. Real number line.
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Dec 13th 2008, 11:53 AM
  5. Replies: 2
    Last Post: Dec 3rd 2008, 06:26 PM

/mathhelpforum @mathhelpforum