0
Two sets are equivalent if they have the same cardinality.
For finite sets it simply means that the two sets have the same number of distinct elements.
Thus {1, 2, 3, 3} is equivalent to {a, b, b, b, b, c, c}; each set has cardinality 3.
For infinite sets, it is a bit more complicated. If you can define a bijective mapping (one-to-one and onto) from the elements of one set to the elements of the other then the two sets are equivalent. By definition, bijective mappings must have an inverse so defining the mapping in one direction is sufficient.
It is relatively easy to see that the set of odd integers is equivalent to the set of even integers if you consider the mapping f(x) = x+1 where x is odd. Or perhaps f(x) = x + 7
What is less obvious is that the set of all integers is equivalent to the set of even integers when you consider the mapping f(x) = 2x where x is any integer.
Thus it is possible for a proper subset of an infinite set to be equivalent to the superset!
Still curious? Ask our experts.
Chat with our AI personalities
Taiga
Vivi
EzraAdd your answer:
Earn +20 pts
What is equivalent of a set?
in a set if two elements or numbers are equal then it is known as equivalent set
What is the equivalent of set?
Two sets are said to be the equivalent if a (1-1)correspondence can be established between them.If set A is equivalent to set B,then we write A is (1-1)correspondence to set B and It shows the quantities of elements.
Which set is equivalent to set M if set M equals 235?
If M = {235} all sets that have only 1 element are equivalent to it
What is an equivalent of a set?
equal sets
Is a set of whole numbers equal to a set of integers or equivalent?
Yes, they are.
