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Question
State the following sets are finite or infinite:
M = {r : r = `3/"n"`; n ∈ W and 6 < n ≤ 15}
Solution
M = {r : r = `3/"n"`; n ∈ W and 6 < n ≤ 15}
r = `3/"n"`
When n = 7,
r = `(3)/(7)`
When n = 8,
r = `(3)/(8)`
When n = 9,
r = `(3)/(9)`
When n = 10,
r = `(3)/(10)`
When n =11,
r = `(3)/(11)`
When n = 12,
r = `(3)/(12)`
When n = 13,
r = `(3)/(13)`
When n = 14,
r = `(3)/(14)`
When n = 15,
r = `(3)/(15)`
∴ M = `{3/7, 3/8, 3/9, 3/10, 3/11, 3/12, 3/13, 3/14, 3/15}`
∴ It is a finite set.
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