Question

2. Determine whether each of these sets is finite, countably

infinite, or uncountable. For those that are countably infinite,
exhibit a one-to-one correspondence between the
set of positive integers and that set.
a) the integers greater than 10
b) the odd negative integers
c) the integers with absolute value less than 1,000,000
d) the real numbers between 0 and 2
e) the set A _ Z+ where A = {2, 3}
f ) the integers that are multiples of 10

Answer 1

a) the integers greater than 10

countable infinite: 1 -> 11; 2 -> 12; 3 -> 13; 4-> 14; 5->15; ...

b) the odd negative integers

countable infinite: 1-> -1; 2-> -3; 3-> -5; 4-> -7; 5-> -9; ...

c) the integers with absolute value less than 1,000,000

finite (-999,999; -999,998; -999,997;...0;...; 999,997;999,998;999,999)

d) the real numbers between 0 and 2

uncountable
e) the set A _ Z+ where A = {2, 3}

finite (it is empty)

f ) the integers that are multiples of 10

countable infinite: 1-> 10; 2-> -10; 3-> 20; 4-> -20; 5-> 30; 6-> -30;...