Equivalent

Definition

Equivalent sets are sets that have the same number of elements. For two sets to be equivalent, there must be a one-to-one correspondence between the elements of both sets.

5 Must Know Facts For Your Next Test

1. Two sets A and B are equivalent if there exists a bijection (one-to-one and onto function) between them.
2. If set A has n elements and set B also has n elements, then A and B are equivalent.
3. Equivalent sets can have different types of elements as long as their cardinalities are the same.
4. The concept of equivalence in sets is related to the idea of cardinality rather than specific membership.
5. In notation, if set A is equivalent to set B, we write A ~ B.

Review Questions

• What condition must be met for two sets to be considered equivalent?
• How do you denote that two sets are equivalent?
• Can two sets with different types of elements be considered equivalent? Why or why not?

Related terms

Cardinality: The number of elements in a set.

One-to-One Correspondence: A relationship where each element of one set pairs with exactly one element of another set.

Bijection: A function that is both injective (one-to-one) and surjective (onto).