Results 1 to 3 of 3

Math Help - Cartesian Product

  1. #1
    Member Ruun's Avatar
    Joined
    Mar 2009
    From
    North of Spain
    Posts
    129
    Thanks
    13

    Cartesian Product

    Hi!

    I'm trying to self-study some math and I've decided to "forget" almost but high school math and start from the beggining.

    I have a seriously easy question about Cartesian Product.

    It is true that (\mathbb{R}^{2} \times \mathbb{R}=\mathbb{R} \times \mathbb{R}^{2}=\mathbb{R}^3) ?

    I've thougth that the first equality is false since the first one is \mathbb{R}^2 \times \mathbb{R}= \{(x,y) : x \in \mathbb{R}^2 and y \in \mathbb{R} \} and in the second one \mathbb{R} \times \mathbb{R}^2 = \{(x,y) : x \in \mathbb{R} and y \in \mathbb{R}^2 \} but then I thought that both are equal to \mathbb{R}^{3}.



    Thanks in advice

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,415
    Thanks
    1853
    Quote Originally Posted by Ruun View Post
    Hi!

    I'm trying to self-study some math and I've decided to "forget" almost but high school math and start from the beggining.

    I have a seriously easy question about Cartesian Product.

    It is true that (\mathbb{R}^{2} \times \mathbb{R}=\mathbb{R} \times \mathbb{R}^{2}=\mathbb{R}^3) ?

    I've thougth that the first equality is false since the first one is \mathbb{R}^2 \times \mathbb{R}= \{(x,y) : x \in \mathbb{R}^2 and y \in \mathbb{R} \} and in the second one \mathbb{R} \times \mathbb{R}^2 = \{(x,y) : x \in \mathbb{R} and y \in \mathbb{R}^2 \} but then I thought that both are equal to \mathbb{R}^{3}.



    Thanks in advice

    Strictly speaking, no, they are not the same.
    R^2\times R= \{((x,y),z)\}
    R\times R^2= \{(x, (y,z))\}
    R^3= \{(x, y, z)\}

    However, there is an obvious correspondence between any two of them. Further, with the various operations (pointwise addition, etc.) that we can define on them, that correspondence becomes an isomorphism.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Ruun's Avatar
    Joined
    Mar 2009
    From
    North of Spain
    Posts
    129
    Thanks
    13
    Right, solved, thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cartesian product of A*A*A*A
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 14th 2011, 07:29 AM
  2. Cartesian product.
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: November 4th 2010, 02:59 PM
  3. Cartesian product
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 26th 2010, 12:30 PM
  4. Cartesian Product
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 9th 2010, 12:31 PM
  5. Cartesian Product
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: November 15th 2009, 09:23 AM

Search Tags


/mathhelpforum @mathhelpforum