The main idea of an equivalence relation is that it is something like equality, but not quite. Usually there is some property that we can name, so that equivalent things share that property. For examp...The main idea of an equivalence relation is that it is something like equality, but not quite. Usually there is some property that we can name, so that equivalent things share that property. For example Albert Einstein and Adolf Eichmann were two entirely different human beings, if you consider all the different criteria that one can use to distinguish human beings there is little they have in common.