Lesson 3 of 11 · 7 min
Finite and infinite sets
NCERT §1.4
Two lists: the roll numbers of XI-B who play cricket, and the multiples of 5. You can finish writing the first. However long you write, you never finish the second.
The lesson in notes
In short
n(S) denotes the number of distinct elements of a set S; repeated listings are counted once.
A set is finite if it is empty or has a definite number of elements; otherwise it is infinite.
Finite does not mean small or easy to count: the people living in the world right now form a finite set, while the points on a line, the primes and the multiples of 5 form infinite sets.
Some infinite sets can be shown in roster form with dots, such as N = {1, 2, 3, …} and Z = {…, −2, −1, 0, 1, 2, …}, but not every infinite set can: R has no pattern to list.
Always solve the condition before judging: {x : x ∈ N and (x − 1)(x − 2) = 0} = {1, 2} is finite, {x : x ∈ N and 2x − 1 = 0} = φ is finite, and {x : x ∈ N and x is prime} is infinite.