set notation for vectors of unequal elements

Question

I am looking for a compact way to represent a group of vectors for which each vector contains no two elements that are the same.

$$\textbf{y} \in R^n \quad | \quad y_i \neq y_j \quad \forall \quad y_i, y_j \in \textbf{y}$$

I believe this part $y_i, y_j \in \textbf{y}$, is not correct, I am looking for some way to represent the meaning of an element of a vector

score 2 · Accepted Answer · edited Jul 18 '16 at 12:27

2

what about $\{y\in\Bbb{R}^n| \forall 1 \le i < j \le n, y_i\ne y_j\}$?

edited Jul 18 '16 at 12:27

Ethan Bolker

answered Jul 18 '16 at 12:21

Sagi Shadur

and what are $y_i$ and $y_j$, it is not clarified this way that they are elements in $\textbf{y} $ .. that is the issue behind my question – mahmoud fathy Jul 18 '16 at 12:30
2

$y_i$ is the $i$th coordinate of the vector. it's a well known notation that you can use freely. – Sagi Shadur Jul 18 '16 at 12:33
The notation $\bigl{y\in{\mathbb R}^n,\bigm|,y_i\ne y_j \ (i\ne j)\bigr}$ is even more compact. – Christian Blatter Jul 18 '16 at 13:17
@SagiShadur - So that does mean that I write something like ${\textbf{y} \in R^n \quad | \quad y_i \neq y_j \forall i \neq j \ni 1 \leq i,j \leq n}$ ?!!! ... too good to be true :D. I don't know the rules regarding subscripting. Even if it is not rigorous, It should be understandable anyway. Thanks .. – mahmoud fathy Jul 18 '16 at 14:05

1 Answers1