Mary Jane Sterling - Algebra I All-in-One For Dummies

The absolute value operation, indicated by two vertical bars around a number, , is greatly related to the number line, because it tells you how far a number is from 0 without any regard to the sign of the number. The absolute value of a number is its value without a sign. The absolute value doesn’t pay any attention to whether the number is less than or greater than 0; it just determines how far it is from 0.

The formal definition of the absolute value operation is:

So, essentially, if a number is positive or 0, then its absolute value is exactly that number. If the number you’re evaluating is negative, then you find its opposite — or you make it a positive number.

The factorial operation looks like someone took you by surprise. You indicate that you want to perform the operation by putting an exclamation point after a number. If you want 6 factorial, you write “6!”. Okay, I’ve given you the symbol, but you need to know what to do with it.

To find the value of n !, you multiply that number by every positive integer smaller than n .

There’s one special rule when using factorial: . This is by definition. The value of 0! is designated as being 1. This result doesn’t really fit the rule for computing the factorial, but the mathematicians who first described the factorial operation designated that 0! is equal to 1 so that it worked with their formulas involving permutations, combinations, and probability.

You may have never used the greatest integer function before, but you’ve certainly been its victim. Utility and phone companies and sales tax schedules use this function to get rid of fractional values. Do the fractions get dropped off? Why, of course not. The amount is rounded up to the next greatest integer.

The greatest integer function takes any real number that isn’t an integer and changes it to the greatest integer it exceeds. If the number is already an integer, then it stays the same.

The symbol for the greatest integer function is a set of brackets, . You put your number in question in the brackets, evaluate it, and out pops the answer.

Q.Find the absolute value:

A. . The distance from –4 to 0 is 4 units.

Q.Evaluate:

A. . You perform the operation inside the absolute value bars before evaluating.

Q.Evaluate 3!

A.

Q.Evaluate 6!

A.

Q.Evaluate:

A. . The number 6 is the biggest integer that is not larger than .

Q.Evaluate:

A. . Just picture the number line. The number –3.87 is to the right of –4, so the greatest integer not exceeding –3.87 is –4. In fact, a good way to compute the greatest integer is to picture the value’s position on the number line and slide back to the closest integer to the left — if the value isn’t already an integer.

15 Determine which is greater: or 3!

16 Determine which is greater: or .

17 Determine which is greater: 5! or .

18 Determine which is greater: or .

What is a binary operation ? A bicycle has two wheels. A biannual term lasts two years. And a binary operation requires two numbers. These operations are performed on two numbers — one written before the operation symbol and one after. Addition and subtraction are pretty familiar, but the multiplication and division symbols come in several varieties.

If you’re on an elevator in a building that has four floors above the ground floor and five floors below ground level, you can have a grand time riding the elevator all day, pushing buttons, and actually “operating” with signed numbers. If you want to go up five floors from the third sub-basement, you end up on the second floor above ground level.