- truth values,
- sets,
- relations,
- ternary relations,
- etc;

- constants,
- functions,
- binary functions,
- ternary functions,
- etc.

A **truth value** is either true or false;
any statement with no variables in it should evaluate to true or false.

A **constant** is, in this class, usually just a real number.
Any expression with no variables should evaluate to a constant,
but we use one dimension to graph a constant on a number line.

A **set** is, in this class, a set of real numbers.
A statement with one variable defines a set,
such as {*x* | *x* < 2},
the set of real numbers that are less than 2.
We again use one dimension to graph a set.

A **function** or **unary function** is a rule
for taking one number
(the **input**, or **argument**)
and using it to calculate a number
(the **output**, or **value**).
An example is (*x* → *x* − 2),
the rule which subtracts 2 from any number.
To graph a function, we need two dimensions,
one for the input and one for the output.

A **relation**, or **binary relation**
is a set of ordered pairs instead of a set of individual numbers.
An example
is
{*x*,*y* | *x* + *y* < 2}.

A **binary function**
or **function of two variables**
is a rule
for taking an ordered pair of two arguments
and using it to calculate an output.
An example is
(*x*,*y* → *x* + *y* − 2),
the rule which subtracts 2 from the sum of the arguments.
To graph a binary function, we need three dimensions,
two for the input and one for the output.

We can continue with ternary functions, quaternary functions, etc, which take two or more numbers as inputs; and we can continue with ternary relations, quaternary relations, etc, which relate three or more numbers.

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