Set theory

1 About

2 Inequalities (numbers)

If $a$ and $b$ are numbers, then exactly one of the following is true:

$a < b$
$a > b$
$a = b$

This is called the law of trichotomy.

3 Inequalities (sets)

Sets do not obey the law of trichotomy. For example, none of the following are true:

$\{1\} \subset \{2\}$
$\{1\} \supset \{2\}$
$\{1\} = \{2\}$

4 Here’s a feature

Spaces seem not to matter when you are in math mode. But they do seem to matter when in delimiting of math mode. [Most users will not understand this previous sentence.]

$\{1\}\subset\{2\}$
$ {1} {2}$

5 Union

[This contains the minimum needed to teach the Latex.]

\[ X = A \cup B \]

Words: X equals A union B
Latex: X = A \cup B

6 Intersection

[This contains the minimum needed to teach the math.]

The intersection of two sets $A$ and $B$ are the objects $x$ that are members of $A$ and a member of $B$. The intersection is written as:

\[ X = A \cap B \]

Example: $\{1, 3, 5, 7\} \cap \{3, 5, 9\} = \{3, 5\}$.
Example: $3 \in A$ and $3 \in B$ so $3 \in (A\cap B)$.