Equivalence relation/Equality with respect to a property/Example

In many situations, we are not interested in objects individually, instead, we are interested in some of their specific properties. Objects that behave equally with respect to a certain property might be considered as equivalent (with respect to this property). Such an equality with respect to a certain property defines an equivalence relation. If, for example, we are only interested in the color of some objects, then objects that have (exactly) the same color are equivalent to each other. If we are interested, among a collection of animals, not for their individual properties but only for the species they belong to, then two animals are equivalent if and only if they belong to the same species. Students might be considered as equivalent if they study the same combination of subjects. Vectors can be considered as equivalent if they have the same distance to the origin, etc. An equivalence relation is typically a certain way to look at certain objects, which considers certain objects as equal.