Check if relation is equivalent

In summary, The relation of m~n in Z is not an equivalence relation because it fails to be reflexive due to (0,0) not belonging to the relation.
  • #1
issacnewton
1,041
37
Hello

I have to check if the following relation is an equivalence relation.
\[m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0\]

I think this relation fails to be reflexive since $(0,0)$ does not belong to
this relation. Hence this is not an equivalent relation. Is this ok ?

Thanks
 
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  • #2
IssacNewton said:
Hello

I have to check if the following relation is an equivalence relation.
\[m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0\]

I think this relation fails to be reflexive since $(0,0)$ does not belong to
this relation. Hence this is not an equivalent relation. Is this ok ?

Thanks
Yes. This is good.
 
  • #3
caffeinemachine said:
Yes. This is good.

Thanks
(Emo)
 

FAQ: Check if relation is equivalent

What is an equivalence relation?

An equivalence relation is a mathematical concept that defines a relationship between two objects or sets. It states that the two objects are equivalent if they have the same properties or characteristics, and it follows three main rules: reflexivity, symmetry, and transitivity.

How do you check if a relation is an equivalence relation?

To check if a relation is an equivalence relation, you need to verify if it follows the three main rules: reflexivity, symmetry, and transitivity. This means that the relation must be reflexive (each element is related to itself), symmetric (if A is related to B, then B is related to A), and transitive (if A is related to B and B is related to C, then A is related to C).

What is the importance of checking if a relation is an equivalence relation?

Checking if a relation is an equivalence relation is important because it helps us understand the properties and characteristics of the objects or sets being related. It also allows us to classify the relation and use it in different mathematical operations.

Can a relation be partially equivalent?

No, a relation cannot be partially equivalent. An equivalence relation must satisfy all three main rules (reflexivity, symmetry, and transitivity) in order to be considered equivalent. If even one of these rules is not satisfied, the relation is not considered equivalent.

How can I use the concept of equivalence relation in real life?

The concept of equivalence relation can be used in real life in various ways, such as in computer science for data organization and retrieval, in social sciences for analyzing relationships between variables, and in linguistics for understanding different levels of language proficiency. It can also be applied in everyday situations, such as categorizing objects or people based on shared characteristics.

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