0
For finite sets similarity simply requires both sets to have the same number of distinct elements (the same cardinality). For example, {1,2,3} and {a,b,c,a}. The second set appears to have 4 elements but, in fact, it has only three distinct elements - the same as the first.
Similarity of sets does get more complicated (and counter-intuitive) when dealing with infinite sets. It is probably not too hard to see that the set of odd integers (infinitely many) is similar to the set of even integers (infinitely many). But it is not so easy to see that the set of odd integers is similar to the set of ALL integers.
This is because you can define a mapping from the odd integers to all integers as:
2n-1 to n
Proving that this mapping is bijective (injective and surjective) shows that the two sets have the same cardinality.
Add your answer:
Earn +20 pts
Is it true that all equal sets are equivalent sets?
Yes.
What is equal set from equivalent sets?
equal sets with exactly the same elements and number of elements.equivalent sets with numbers of elements
Can two disjoint sets be equivalent?
Yes,Because not all disjoint no equivalent other have disjoint and 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
What do you call a shape with 2 sets of parallel sides?
A Parallelogram (Examples: Rectangle, square,etc.)
At least 3 examples of equivalent sets?
no
What is the examples of equivalent sets?
A={1,2,3} Z={6,7,2} it is the same number of items
Integer and natural number are equivalent sets if equivalent show that?
They are not equivalent sets.
What is meaning of equivalent sets?
Equivalent sets are sets with exactly the same number of elements.
Are integers and natural numbers equivalent sets?
No, they are not equivalent sets.
Are equivalent sets equal sets why?
No, because equivalent sets are sets that have the SAME cardinality but equal sets are sets that all their elements are precisely the SAME. example: A={a,b,c} and B={1,2,3} equivalent sets C={1,2,3} and D={1,2,3} equal sets
Are all equivalent sets are equal sets?
Yes. Equivalent means equal.
Give you examples of finite sets of numbers?
sets
What is the meaning of equivalent set?
Equivalent sets are sets with exactly the same number of elements.
Is it true that all equal sets are equivalent sets?
Yes.
Definition of equivalent sets?
two sets A and B are said to be equivalent if there exists a bijective mapping between A and B
Are equal sets equivalent set?
yes, equal sets are equalent
