The discussion revolves around the properties of equivalence relations, specifically the symmetric and transitive properties of equality. Participants seek examples that illustrate these properties in a concrete manner rather than abstract generalizations.
Participants do not reach a consensus on the type of examples needed, with some focusing on abstract properties while others seek concrete instances. The discussion remains unresolved regarding the clarity of the original request for examples.
Some participants express confusion over the distinction between properties and examples, indicating a potential limitation in the clarity of the questions posed.
Given a, b, and cpaulmdrdo said:can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!
Are you thinking of something along the lines ofpaulmdrdo said:no. that's the generalize form. i want an example where you can apply the properties.
paulmdrdo said:can you give an example of symmetric property of equality and transitive property of equality.
topsquark said:Are you thinking of something along the lines of
R = {(0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)}
and then determining if R is symmetric and/or transitive?
Hmm. OP, you seem to ask not for an example of a property of equality, but for an example of equality, and, in fact, not of equality, but of an arbitrary relation. I know what an example of an object (e.g., a car) is and what an example of an object with some property (e.g., a red car) is, but I don't know what an example of a property is (what is an example of red?). Formulating your questions precisely is half the answer.paulmdrdo said:yes!