Mathematics
State whether the given set is finite or infinite :
(i) Set of all even natural numbers.
(ii) Set of all odd integers.
(iii) Set of all rivers in India.
(iv) Set of all points on a line segment 1 cm long.
(v) Set of all factors of 1200.
(vi) Set of all multiples of 6.
(vii) Set of all drops of water in a bucket.
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Answer
(i) Set of all even natural numbers.
Natural numbers go on forever (2, 4, 6, 8, …..), so the counting process never ends.
∴ It is an infinite set.
(ii) Set of all odd integers.
Integers extend infinitely in both positive and negative directions (…., -3, -1, 1, 3, ….).
∴ It is an infinite set.
(iii) Set of all rivers in India.
Although there are many rivers, the total number is a specific, countable figure that can be listed.
∴ It is a finite set.
(iv) Set of all points on a line segment 1 cm long.
Mathematically, a line segment consists of an uncountable infinity of points, regardless of its length.
∴ It is an infinite set.
(v) Set of all factors of 1200.
Every number has a limited (finite) number of factors.
∴ It is a finite set.
(vi) Set of all multiples of 6.
Multiples are generated by multiplying 6 by natural numbers (6, 12, 18, ….), which are endless.
∴ It is an infinite set.
(vii) Set of all drops of water in a bucket.
The number is extremely large and difficult to count.
∴ It is an infinite set.
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