Lesson 4 of 11 · 8 min
Equal sets
NCERT §1.5
Priya writes the cricket list in roll order. Kabir writes it in the order people signed, with roll 12 written twice by mistake. Have they written different sets?
The lesson in notes
In short
Two sets A and B are equal, A = B, when they have exactly the same elements: every element of A is in B and every element of B is in A. Otherwise A ≠ B.
Order and repetition never matter: {1, 2, 3} = {3, 3, 2, 1}, and the letters of LISTEN and of SILENT give the same set {L, I, S, T, E, N}.
One element that lies in one set and not the other is enough to prove the sets unequal: {x : x ∈ Z, x² = 9} = {−3, 3} is not equal to {x : x ∈ N, x² = 9} = {3}, because −3 is in the first only.
The same set can be described in very different words: the prime factors of 60 and the primes less than 7 are both {2, 3, 5}.
Equal sets always have the same number of elements, but having the same number of elements does not make two sets equal: {1, 2} ≠ {a, b}.