Download Homework for the Set of Real Numbers

Real Numbers
1.
From the list
{ 2, 3/5, √2 , 𝜋, .35, 6.45, 0,
6
,
0
Identify which ones are
a) Integers
b) Rational
−2, .25465781931.. , .262626 … ,
c) Irrational
0
0
, √16 }
d) Real
2.
Determine if the statement is True or False.
a) Any Natural number is an Integer.
b) Any Integer is a Rational number.
c) A Real number can be only Irrational.
d) A terminating decimal is an Irrational number.
e) 0/5 = 0
f) A Rational number can be either a terminating decimal or non-terminating decimal with a
repeating pattern.
3.
4.
5.
6.
State the set of integers.
State the set of integers between -4 and 8.
State the set of all natural numbers that are multiples of 5.
State the even natural numbers.
7. Determine if √−9 is a real number.
8. Put a check mark in each box if the number is a member of that set.
Naturals
Integers
Rational
Irrational
0
18
√6
9. Express the set of all real numbers using interval notation.
10. Express the set of all real numbers greater than or equal to zero.
11. Express the set of all real numbers less than or equal to 4
5
12. Explain why 0 is not a real number.
Real
Solutions:
1. a) 2, 0, -2, √16
b) 2, 3/5 , .35, 6.45, 0, -2 , .26262626…, √16
√2 , 𝜋, .25465781931 …. d) All of them except
2.
3.
4.
5.
6.
7.
8.
6
0
a) True b) True c) False d) False e) True f) True
… -3, -2, -1, 0, 1, 2, 3, …..
-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7
5, 10, 15, 20, 25, …..
2, 4, 6, 8, 10, …..
No it is not real. Why?
A) 0 is an integer , rational and real.
B) 18 is a natural, integer, rational and real.
C) √6 is irrational and real.
9. (−∞, ∞) or −∞ < 𝑥 < ∞
10. [ 0, ∞)
11. (−∞, 4]
𝑎𝑛𝑑
0
0
c)