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

[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?


Thank you for your help.

M

 

[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.

 

[Mark44]

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?


Thank you for your help.

M

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.

 

[Mark44]

Well $$R$$ usually just denotes the real plane

No, R does not represent 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.

 

[Asphyxiated]

real number line/set of real numbers. sorry

 

[michonamona]

Excellent, thanks guys.