tivity. Again, not all operations are distributive. For example, addition is not distribu-
tive over multiplication, as in a(bc) (ab) (ac).
What is the factorialof a number?
A factorial is the product of consecutive natural numbers for all integers greater than
or equal to 0. Factorials usually start with 1; the symbol for factorial is an exclamation
point (!). For example, 4 factorial (4!) is 1 2 3 4, or 24. In the numerical sys-
tem, consecutive factorials are 1 (1! 1), 2 (2! 1 2), 6 (3! 1 2 3), 24 (4!
1 2 3 4), 120 (5! 1 2 3 4 5), 720 (6! 1 2 3 4 5 6),
5040 (7! 1 2 3 4 5 6 7 ), 40,320 (8! 1 2 3 4 5 6 7
8), 362,880 (9! 1 2 3 4 5 6 7 8 9), and so on.
There are two additional rules: The number 0 factorial (0!) 1, and the factorial
values for negative integers are not defined. Factorials are most often used in refer-
ence to counting numbers, statistics (especially in probability calculations), calculus,
and physics.
EXPONENTS AND LOGARITHMS
What is an exponentin terms of algebra?
An exponent is actually raising a number to a certain power; this is written as a super-
script to the right of a real number, such as 3^4 (expressed as “three raised to the fourth 143
ALGEBRA
What does iteration mean?
I
n most English texts, iteration means to repeat, and this holds true for mathe-
matics. In the case of numbers, iteration means a procedure in which the
result is fed back and the procedure repeated; in some instances, it is repeated
over and over. For example, to find the square root of 39, you can use iteration—
or repeat a procedure to find the solution. Knowing that the solution must be
close to 6 (or the square root of 36, a number close to 39), one can divide 39 by 6
(39/6) and get 6.5. Next, average 6 and 6.5 to get 6.25; then iterate again, divid-
ing 39 by 6.25 (39/6.25) 6.24 (the actual square root of 39 is 6.244997 ...).
One of the most obvious instances in which iterations take place is in a cal-
culator or computer. For example, in order to get the square root of 39, as in the
example above, a calculator (or computer) automatically uses iteration to calcu-
late the answer to a certain decimal place. The more numbers in a procedure,
the more iterations are needed, which is why supercomputing has become such
a great asset not only to mathematics but many other sciences as well.