How Real Variables Behave
Most of the properties of the natural numbers, integers, and rationals also apply to the reals.
To get ready for the algebra to come, let’s put together a collection of these properties. All the
old rules are here, along with a few new or expanded ones. Don’t try to memorize these rules.
Just look them over for a little while. You can always come back to this section for reference
if you get stuck later on.
Naming variables
You’ll notice that some of the variables here have different letter names than we used before.
In algebra, real variables are usually given letters from near the end of the alphabet, especially
t and after. Other letters more often represent natural-number variables (n and m are espe-
cially common), integer variables, and rational-number variables. But there’s no absolute law
about this.
Additive identity
For every real number x,
x+ 0 =x
and
0 +x=x
Multiplicative identity
For every real number x,
x 1 =x
and
1 x=x
Additive inverse
For every real number x,
x+ (−x)= 0
and
(−x)+x= 0
How Real Variables Behave 133
