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Two sets are equivalent if they have the same cardinality. For finite sets this means that they must have the same number of distinct elements. For infinite sets, equal cardinality means that there must be a one-to-one mapping from one set to the other.
This can lead to some counter-intuitive results. For example, the cardinality of the set of integers is the same as the cardinality of the set of even integers although the second set is a proper subset of the first. The relevant mapping is x -> 2x.
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What is the definition of equivalent inequalities?
The definition of equivalent inequalities: inequalities that have the same set of solutions
When two fraction name the same part of a region or a set they are called?
equivalent
Do all infinite sets are equivalent sets?
we can consider all infinite sets as equivlent sets if we go by the the cantor set theory.for eg. on a number line if we consider the nos. between 0 and 1 as a set then they are infinite. similarly the nos. between 0 and 5 can also be considered infinite and if considered as a set then they can be considered as equivalent
If two sets are equal are they necessarily equivalent?
T, The set of integer geater than requal to negative five
What is equal set from equivalent sets?
equal sets with exactly the same elements and number of elements.equivalent sets with numbers of elements
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.
What is Equivalent Set in Math?
When two set have the same number of cardinately
What is the definition of equivalent sets?
Two sets are said to be equivalent if the elements of each set can be put into a one-to-one relationship with the elements of the other set.
What is the definition of equivalent inequalities?
The definition of equivalent inequalities: inequalities that have the same set of solutions
What is the meaning of equivalent set?
Equivalent sets are sets with exactly the same number of elements.
What is equal and equivalent set?
Two sets are equal if they have the same elements. Two sets are equivalent if there is a bijection from one set to the other. that is, each element of one set can be mapped, one-to-one, onto elements of the second set.
If a set A is equivalent to a subset of B and B is equivalent to a subset of A then show that A is equivalent to B?
This problem can be modeled and tested quite easily. Set A can be [X,Y], subset B [X,Y], and subset A [X,Y]. Therefore A and B are equivalent.
Why equal set are equivalent set but equivalent set are not equal set?
Two sets are equivalent if they have the same cardinality. In [over-]simplified terms, if they have the same number of distinct elements. Two sets are equal if the two sets contain exactly the same distinct elements. So {1, 2, 3} and {Orange, Red, Blue} are equivalent but not equal. {1, 2, 3} and {2, 2, 2, 3, 1, 3} are equal.
