Review of Mathematical Symbols

__Symbols__

x and · are both used to express multiplication. So 3 x 4 = 12, and 2 · 3 = 6.

Inequality is expressed with the < “less than” or > “greater than” sign. Signs are sometimes combined; ³ means “greater than or equal to”.

Absolute value is symbolized by vertical lines surrounding the value, such as êa ê. This means that regardless of the sign of a, its absolute value is positive. ê-3 ê= 3.

The Greek capital sigma, S, is used to indicate a
summation. S a_{i} tells you
to add all of the values in a set of a’s, a_{1} + a_{2} + a_{3}
+ a_{4} + ... where the number of a values is not specified.

P__owers__ (Exponents)

k^{n} is
read is “k to the n-th power”. n is
referred to as the exponent, while k is referred to as the base. k^{n} means that you should multiply
k by itself n times to get the answer.
Squaring, or taking k to the second power, is the most familiar
example. 3^{2} = 9. If your calculator has an “x^{y}”
button, you can do the operation quickly.
Enter the value of k, then hit the “x^{y}” button, then enter
the value of n, then hit the “=” button.
If your calculator does not have the specialized button, you can still
get the desired value by entering the value of k, then hitting the “x”
(multiply) button. Then hit the “=” button n times.

When you multiply
two values that have the same base, such as 3^{2} x 3^{3}, you
can save some arithmetic by adding the exponents – the answer is equal to 3^{5}. When you multiply two values that have
different bases, you need to find each power separately, then multiply the
results. 2^{3} x 3^{3}
= 4 x 27 = 108.

Any base to the
0th power, such as 3^{0 }or 500^{0}, is equal to 1.

__ __

The factorial operation is a shorthand way of expressing the product of a positive integer and all of the integers below it. Its symbol is an exclamation point. 5! = 5 x 4 x 3 x 2 x 1 = 120. 0! is special – it is equal to 1.