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

1. May 2, 2010

### michonamona

Hello everyone,

What does my professor mean when he says x belongs in $$R^{n}$$. What is $$R^{n}$$?

Does $$R^{1}$$ mean 1-variable? or 2-dimension (just a line)? or both?

What about $$R^{2}$$? is this 2 variable? or 3-dimension? both?

M

2. May 2, 2010

### Asphyxiated

Well $$R$$ usually just denotes the real plane as opposed to $$C$$ which is the complex plane. if you have $$R^{2}$$ and $$R^{3}$$ 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.

3. May 2, 2010

### 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.

4. May 2, 2010

### Staff: Mentor

No, R does not represent the real plane.

5. May 2, 2010

### Asphyxiated

real number line/set of real numbers. sorry

6. May 2, 2010

### michonamona

Excellent, thanks guys.