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

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Homework Help Overview

The discussion revolves around the notation R^n, specifically the meanings of R^1, R^2, and R^3 in the context of dimensions and variables. Participants are exploring the definitions and implications of these notations in relation to real numbers and dimensional spaces.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the meanings of R^1, R^2, and R^3, specifically whether they refer to dimensions or variables. There is also discussion about the implications of these notations in different mathematical contexts.

Discussion Status

Some participants have provided definitions and clarifications regarding the dimensionality of R^n, while others express uncertainty about the context in which these notations are being used. Multiple interpretations are being explored without a clear consensus.

Contextual Notes

There is a noted confusion regarding the definitions of R, R^1, R^2, and R^3, as well as their applications in various mathematical subjects. The discussion reflects a need for clarity on the relationship between dimensionality and the number of variables.

michonamona
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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
 
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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.
 
michonamona said:
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
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.
 
Asphyxiated said:
Well [tex]R[/tex] usually just denotes the real plane
No, R does not represent the real plane.
Asphyxiated said:
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.
 
real number line/set of real numbers. sorry
 
Excellent, thanks guys.
 

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