0
$\begingroup$

A statement like the following is called an equality: $$ 2 + 2 = 4 $$

In contrast, a statement like the following is called an inequality:

$$ 2 + 2 < 5 $$

One can refer to groups of these statements with phrases like "We list several important equalities below" or "Recall the inequality on the previous page".

Is there a name for statements like this, indicating inclusion in a set? $$ x \in \mathbb{X} $$

Specifically, it would be nice to know if there is a name that can be used to refer to groups of these statements.

I considered "definition" but if one has defined the member of the set (say, $x$ from the previous example) is a different way already, and one wishes to express that $x$ is a member of some, also previously defined, set, then "definition" doesn't work. One could the generic term "lemma" or use "statement" as I have been in this question, but I'm curious if there is another, more specific term.

The question of whether there is a similar name for statements like this, indicating exclusion from a set arises naturally, as well:

$$ y \notin \mathbb{X} $$

$\endgroup$
1

1 Answer 1

4
$\begingroup$

Maybe "membership" for $x\in X$.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .