Question

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

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;...