The Set of Real Numbers

Question 1

What is a Real Number (R) ?

Answer 1

The type of number we normally use, such as 1, 15.82, -0.1, 3/4, etc…

Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.

Real Numbers (R) are either Rational (Q) or Irrational (I). R = Q U I

Natural Numbers are contained in the Integers,contained in the Rationals, contained in the Reals –> N c Z c Q c R

Question 2

What is the Set of Real Numbers (R) ?

Answer 2

The Natural Numbers (N) - the counting numbers, N = { 1, 2, 3,…}

The Integers (Z) = all the Natural Numbers negative, positive and zero, Z = {…-2, -1, 0, 1, 2,…}

The Rational Numbers (Q) = fractions or ratios of Integers, Q = a/b, b is not 0, and a and b are integers

Question 3

What two type of decimals exist in Rational Numbers (Q)?

Answer 3

1/2 = 0.5 Terminates 
1/3 = 0.33333... Repeats

Question 4

What is an Irrational Number (I) ?

Answer 4

Real Numbers (R) that are not Rational (Q)

I =

Question 5

Let S = {-squareroot(sr)5, -1, π, 3/4,3, sr7, 10, -sr4, 0, sr81/4}.

Which are

a) Natural (N)
b) Integer (Z)
c) Rational (Q)
d) Irrational (I)

Answer 5

a) Natural Numbers (N)
N = { 3, 10}

b) Integers (Z)
Z = {-1, 3, 10, 0, -sr4 (which is -2)}

c) Rational (Q)
Q= {-1, 3/4, 3, 10, 0, -sr4 (same as-2), sr81/4 (same as sr81/sr4 = 9/2)}
N.B (3 and 10 are the same as 3/1 and 10/1)

d) Irrational (I)
I = {-sr5, π, sr7}