Elementary question: distinct elements in a set [closed]

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

I'd like to know the syntax for describing a number of elements in a set, and that each of them are distinct. e.g.

{$x,y,z$} $\in A$

I would like to know how I can succinctly express the following, without having to write it out as such:

$x \neq y \;\;\;\; x \neq z \;\;\;\; y \neq z$

-

4
"Brevis esse laboro, obscurus fio." (Horace) – François G. Dorais♦ Feb 3 at 18:33

2
For three elements, $x\neq y\neq z\neq x$ expresses the inequalities in 7 symbols. For four elements, this linear-string approach takes 15. For five, it can be done in 21, and in general, for any odd number $n>1$, it can be done in $n(n-1)+1$ symbols (although I suppose you might run into trouble at $n=27$). Curiously, the OEIS does not (yet) have an entry extending $3,7,15,21$ with both $43$ and $73$ in the proper place. – Barry Cipra Feb 5 at 17:53

4 Answers

"Let $x,y,z,$ be pairwise distinct", is perfectly fine.

-

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.

"Let $x, y, z$ be distinct" is enough.

-

"Let $\lbrace x,y,z \rbrace$ be a set with exactly three elements."

-

{x,y,z} $\cong3$ or |{x,y,z}| $=3$

-
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.915522038936615, "perplexity_flag": "middle"}