They are mentioned as important pointers below. Now let us expand our knowledge to accommodate a few fascinating facts about the relation between equal and equivalent sets. We are now clear on what equal and equivalent sets are. If M=, it can be noted that both Set G and Set H comprise word elements in different categories and have the same number of elements i.e. Let’s understand equal sets with an example, If we consider numbers to denote the elements of two sets then we can understand equal and equivalent sets in the following manner.

The sets don't need to hold the same elements, or they stay to be a subset of each other. Therefore, in general, it can be stated that the two sets remain equivalent to each other if only the number of elements in both the sets remain equal. In this context, the one to one condition implies that for each element on the set A, there exists an element in the set B, till both the set A and set B gets exhausted. This condition means that there should be one to one correspondence between the elements belonging to both the sets. In other words, if there is a basket of apples and a basket of oranges, then if they are of the same number, we can call these as an example for equivalent sets. Thus, to remain or be equivalent, the sets should possess the same cardinality. To elaborate, if the two baskets contained an unequal number of oranges or if one basket contained apples and the other contained oranges of the same number, then these cases are said to be examples for unequal sets.Įquivalent sets meaning in Mathematics holds two definitions.Įquivalent Sets Definition 1 - Let's say that two sets A and B have the same cardinality, then, there exists an objective function from set A to B.Įquivalent Sets Definition 2 - Let's say that two sets A and B are stated to be equivalent only if they have the same cardinality, that is, n(A) = n(B). It is to be noted that if the condition discussed above is not met, then the set is stated to be unequal. Also, if two sets happen to be the subsets of each other, then they are stated to be equal sets.Ĭontinuing our above example, if we were to compare one basket of oranges with another basket of oranges, and if the number of oranges is equal in both the baskets, then this is said to be an example for equal sets. Two sets A and B can be equal only on the condition that each element of set A is also the element of set B. To understand Equal Set meaning, Equal Set is defined as two sets having the same elements. The same way, if we were to compare two sets, we could use cardinality as a standard for comparison.

Or we could say that there are equal numbers of apples and oranges. If we were to compare them by number, then we could say that there are more apples than oranges or vice versa. Like how you would compare apples to oranges but if there is no standard by which we can compare them, then it would be very difficult to establish anything. You may think of this as some sort of comparison. Now this is important because this will help us understand the difference between equal and equivalent sets.Įqual and equivalent sets are terms used to denote some kind of relationship between two sets. Cardinality is the number of elements inside a set. These two are similar concepts, yes, but there is a minor difference between them that sets them both apart.īut before we divide into equal and equivalent sets, let us understand what cardinality is. Even though equal and equivalent sets sound like there isn’t much difference between them.

Equ and equal definition