I have a set of nonzero vectors in RR^n, where for each vector, its nonzero elements have the same magnitude. For example, when n=4, (1,0,1,0) and (−3,3,0,3) are in this set, while (1,2,3,2) and (0,0,0,0) are not. The formal notation I came up for it is {x in RR^n∣x != 0 text( and ) x_i in {0,k,−k} text( for some ) k in R} but I'm not sure if the "for some k" part is correct. Should it be "for all k" instead?

ghulamu51

ghulamu51

Answered question

2022-09-19

I have a set of nonzero vectors in R n , where for each vector, its nonzero elements have the same magnitude. For example, when n = 4, ( 1 , 0 , 1 , 0 ) and ( 3 , 3 , 0 , 3 ) are in this set, while ( 1 , 2 , 3 , 2 ) and ( 0 , 0 , 0 , 0 ) are not.
The formal notation I came up for it is
{ x R n x 0  and  x i { 0 , k , k }  for some  k R } ,
but I'm not sure if the "for some k" part is correct. Should it be "for all k" instead?

Answer & Explanation

Elias Keller

Elias Keller

Beginner2022-09-20Added 11 answers

If you say " x i { 0 , k , k } for all k R " then you say that x i belongs to every { 0 , k , k }, which is not possible unless x i = 0.. And you do not want that for every i.
What you wrote is OK but could be mis-interpreted.
You could also write { x R n : x 0 k R i ( x i { 0 , k , k } ) } .
If you want to be annoyingly rigorous but still right, you could write k R ( { 0 , k , k } n ) { 0 } n .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?