Can R^2 Represent Planes Other Than the xy Plane in R^3?

Thread starter loli12
Start date Sep 5, 2005
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Plane

AI Thread Summary

R^2 can represent planes other than the xy plane in R^3, as it is defined as a two-dimensional space that can exist in various orientations. The discussion centers on the definition of W as the xy plane, which is a specific instance of R^2 in R^3. The claim that R^2 can only represent the xy plane is contested, as R^2 can theoretically be positioned anywhere in three-dimensional space. The book's assertion that the statement is false may stem from a misunderstanding of the flexibility of R^2's placement. Ultimately, R^2's definition allows for the possibility of representing multiple planes in R^3.

Sep 5, 2005

loli12

Can R^2 be planes other than the xy plane if it is not defined?
Because I got this statement which the book claims it to be false.

Let W be the xy plane in R^3; that is, W={(a1, a2, 0):a1, a2 from R). R= field of real numbers. Then W=R^2.

is there any other reason to make this statement false?

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Sep 5, 2005

whozum

R2 is just a two dimensional plane, you can put it anywhere you want.

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