Question

State which of the following sets are finite and which are infinite. Give reasons for your answer. 

i) A = {x : x e N and x < 100} 

ii) B = {x : x e N and x ≤ 5} 

iii) C = {1² , 2² , 3³ , ……} 

iv) D = {1, 2, 3, 4} 

v) {x : x is a day of the week}

Answer 1

i) A = (1, 2, 3, 4, , 98, 99} This set is finite, because there are 99 numbers possible to count. 

ii) B = {1, 2, 3,  4, 5} This set is finite because there are 5 numbers possible to count. 

iii) C = {1², 2², 3², ……} This set is infinite because there are infinite numbers. 

iv) D – {1, 2, 3, 4} This set is finite because there are 4 numbers that are possible to count. 

v) E = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} This set is finite, because there are 7 days in a week possible to count.