Question

Is 2-space a subset of 3-space? If so, why? I thought it would be, but my text says it's not, but doesn't justify.

Answer 1

Because the vectors in R^3 all have three elements (i.e. they are all of the form (a,b,c) ). In contrast, the vectors in R^2 only have two elements apiece (they're of the form (x, y) ). So it's like comparing apples and oranges. Make sense??

Answer 2

Thanks. That makes sense.