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A question on notation - R^1, R^2, ,R^n

  1. May 2, 2010 #1
    Hello everyone,

    What does my professor mean when he says x belongs in [tex]R^{n}[/tex]. What is [tex]R^{n}[/tex]?

    Does [tex]R^{1}[/tex] mean 1-variable? or 2-dimension (just a line)? or both?

    What about [tex]R^{2}[/tex]? is this 2 variable? or 3-dimension? both?


    Thank you for your help.

    M
     
  2. jcsd
  3. May 2, 2010 #2
    Well [tex] R [/tex] usually just denotes the real plane as opposed to [tex] C [/tex] which is the complex plane. if you have [tex] R^{2} [/tex] and [tex] R^{3}[/tex] it could be different sets in set theory but I am not sure what you are working on right now. Depending on the subject of study it could be completely different than that.
     
  4. May 2, 2010 #3

    Mark44

    Staff: Mentor

    R or R1 is a one-dimensional space of real numbers - the real number line. A single coordinate suffices to locate a point on a line. You are apparently confused about the dimension of a line.

    R2 or R X R is a two-dimensional space of pairs of real numbers - the real plane. A point or vector in R2 has two coordinates.

    R3 or R X R X R is a three-dimensional space of triples of real numbers. A point or vector in R3 has three coordinates.

    Rn is an n-dimensional space of n-tuples of real numbers. A point or vector in Rn has n coordinates. Although we have a hard time imagining spaces of more than three dimensions, most of the concepts we understand from one-, two-, or three-dimensional space extend naturally to a space of n dimensions.
     
  5. May 2, 2010 #4

    Mark44

    Staff: Mentor

    No, R does not represent the real plane.
     
  6. May 2, 2010 #5
    real number line/set of real numbers. sorry
     
  7. May 2, 2010 #6
    Excellent, thanks guys.
     
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