For each of the following sets, identify whether the size (or to be technical, \

Question

For each of the following sets, identify whether the size (or to be
technical, "cardinality") of the set is finite, infinite-and-countable, or infinite-anduncountable.
Explain your answer in each case. If the set is finite, write an expression
that gives the number of items in the set.
a. The set of all rational numbers between 0 and 0.001
b. The set of all irrational numbers between 0 and 0.001
c. The set of all distinct ways of ordering a deck of 52 cards such that all hearts occur
before any other card. (That is, the first 13 cards are all hearts.)
d. The set of all ways of choosing a Mastermind code that uses the color orange exactly
once.
e. The set of all possible ways of assigning either 0 or 1 to a countably infinite number of
slots. (Another way of thinking about this: how many possible infinite-length binary
numbers can you write?)
f. The set of all perfect squares (1, 4, 9, 16

Explanation / Answer

a. The set of all rational numbers between 0 and 0.001 --Infinite and uncountable

b. The set of all irrational numbers between 0 and 0.001 -- Infinite and uncountable

c.. The set of all distinct ways of ordering a deck of 52 cards such that all hearts occur -- Finite and countable

d. The set of all ways of choosing a Mastermind code that uses the color orange exactly

once. -- Finite and countable

e. The set of all possible ways of assigning either 0 or 1 to a countably infinite number of
slots. (Another way of thinking about this: how many possible infinite-length binary
numbers can you write?) -- Infinite and countable

f. The set of all perfect squares (1, 4, 9, 16

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