victorrodriguez / computational-methods Goto Github PK

In the README.md file of the lab 01 it is said: “Let R a binary relation on a set A. […] R is an equivalence relation if A is nonempty and R is reflexive, symmetric and transitive.”. Although this statement is true, the additional condition "A is non-empty" does not affect the truth of the statement since the condition holds whether A is empty or not.

In my opinion, adding this condition could make the reader believe that even if R were reflexive, symmetric, and transitive, it would not be of equivalence if A were an empty set, which is false. Therefore, I think it would be appropriate and clarifying to change the text to: “Let R a binary relation on a set A. […] R is an equivalence relation if and only if R is reflexive, symmetric and transitive.”

This is important because it clarifies the expected output for the case in which the input is an empty relation on an empty set (which is reflexive, symmetric, transitive, and of equivalence).