The set of the natural numbers (also known as counting numbers) contains the
elements,
The set of whole numbers includes all the elements of the natural numbers plus
the number zero (0).
The set of integers includes all the elements of the set of whole numbers and the
opposites or “negatives” of all the elements of the set of counting numbers.
The set of rational numbers includes all numbers that can be written as a
fraction or as a ratio of integers. However, the denominator cannot be equal to
zero.
a) Irrational numbers are numbers that cannot be written as a ratio of two
integers. This description is exactly the opposite that of the rational numbers.
b) Irrational numbers are the leftover numbers after all rational numbers are
removed from the set of the real numbers. You may think of it as,
irrational numbers = real numbers “minus” rational numbers
c) Irrational numbers if written in decimal forms don’t terminate and don’t
repeat.
A. List the elements in each of the sets described in
each item.
= {O, 1, 2}
= {-1, O, 1, 2, 3, 4}
= {1, 2, 3}
= {1, 2, 3, 4}
= {± 5}
B. Answer True or False.
1. Every whole number is an integer.
TRUE
2. Every integer is a whole number.
FALSE
3. Every integer is a rational number.
TRUE
4. Every rational number is an integer.
FALSE
5. Every real number is a rational number.
FALSE
B. Answer True or False.
6. Every irrational number is a real number.
TRUE
7. Every real number is a complex number.
TRUE
8. Every real number is a rational or an irrational number.
TRUE
9. Every point on the number line can be associated with a real number.
TRUE
10. A fraction is an irrational number.
FALSE