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  1. 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.

Athe integers greater than 10
Bthe odd negative integers
Cthe integers with absolute value less than 1,000,000
Dthe real numbers between 0 and 2
Ethe set A _ Z+ where A = {2, 3}

f ) the integers that are multiples of 10

Verified Answer :

Edufirst
Athe 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;...

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