Question

Determine whether each of these sets is countable oruncountable. For those that are countably infinite, exhibit

Answer 1

Answer:

Answers are given below.

Step-by-step explanation:

a) one-to-one correspondence between the set of positiveintegers and that set.

Whenever we have one to one correspondence with positive integers, the set is countable and here infinite.

b) integers divisible by 5 and not 7 ..This set is all integers divisible by 5 but not by 7.  This is a discrete set and hence countable and infinite.

c) the real numbers with decimal representationsconsisting of all 1’s

-- This cannot be counted and hence uncountable but infinite.

d) the real numbers with decimal representationsconsisting of all 1’s or 9’s

-- This is also uncountable but infinite.