Question about notation (hyperplanes)

[Gusbob]

Homework Statement

I have a question for which I'm supposed to show that a function maps into "a hyperplane {u in ℝ⁵:u⁵=1}".

Does this mean that the target space is the set of vectors in ℝ⁵ such that the dot product of u with itself (5 times) is 1? Doesn't seem right...

Any clarification is appreciated.

EDIT: I think I figured it out. The u^5 is meant to denote the 5th coordinate, which makes a lot of sense in my case. Thank you for reading anyways.

 

[HallsofIvy]

That's right. This is the "plane" of all points of the form (a, b, c, d, 1).

 

[Mark44]

Did the original problem use superscripts (u⁵) or subscripts (u₅)? The latter form would make it clearer that it's talking about the 5th coordinate of a vector in R⁵, rather than the 5th power of some number u.