Algebra Know-It-ALL

If we remember the basic multiplication sign rules, we can see that

− 100 =− 5 × 5 × 2 × 2

This same technique can be applied to any negative nonprime number smaller than −3 to show that it’s

composite! We have to be sure that “negative primes” are allowed in the mathematical system we’re deal-

ing with. According to the traditional definition, all the primes are natural numbers larger than 1, so this

trick won’t work.

Practice Exercises

This is an open-book quiz. You may (and should) refer to the text as you solve these problems.

Don’t hurry! You’ll find worked-out answers in App. A. The solutions in the appendix may not

represent the only way a problem can be figured out. If you think you can solve a particular

problem in a quicker or better way than you see there, by all means try it!

1. If the number 0 is the set containing nothing, then what number does nothing represent?


2. The number 3 is odd. If a number n is divisible by 3 without a remainder, does that
   meann must be odd?


3. When an odd number is multiplied by 3, is the result always odd? If so, demonstrate
   why. If not, show a counterexample (a situation where an odd number is multiplied by 3
   to get an even number).

0

1

2

3

1

2

• 3


• 
  
  
  
  • 
    
  
  
  
  

Larger according

to the traditional

definition

Smaller according

to the traditional

definition

Smaller

negatively

Larger

positively

Smaller

positively

Larger

negatively

Figure 3-6 This drawing, and careful choice of words, can help you

avoid confusion when comparing the values of integers.

Practice Exercises 49