Algebra/Chapter 2/Solutions

Answer to Q2.12

Answer to Problem 2.13

a. Real, Rational, Integer, Whole, Natural

b. Real, Rational, Integer
c. Real, Rational, Integer, Whole
d. Real, Rational
e. Real, Rational
f. Real, Rational
g. Real, Rational
h. Real, Irrational
i. Real, Rational, Integer, Whole, Natural
j. Real, Rational
k. Real, Rational
l. Real, Rational
m. Real, Irrational
n. None
o. Real, Irrational
p. Real, Rational, Integer, Whole, Natural
q. Real, Rational
r. Real, Rational, Integer
s. Real, Rational, Integer
t. Real, Irrational
u. Real, Rational, Integer, Whole
v. Real, Irrational
w. Real, Rational
x. Real, Rational

y. Real, Irrational

Solution to P2.41

Let's choose a number between 0 and 1, in this case ${\frac {1}{2}}$. Then we can choose a number between 0 and ${\frac {1}{2}}$, ${\frac {1}{4}}$, and a number between ${\frac {1}{2}}$ and 1, ${\frac {3}{4}}$. We can keep going beyond this point, and we will still always find a number between any two numbers we choose. Therefore, there are infinitely many real numbers between 0 and 1.