(1) An "infinite set" is consisted by a kind of "infinite elements (infinite carriers)" ------- there will be no "infinite set" without "infinite carriers".
(2) The unique characteristics (special properties, special existing conditions, special form of expression and the special relationship between and among each other) of each kind of “infinite carriers (infinite elements)” constitute each "unique infinite set"-------- there will be no variety of different infinite sets without "different kinds of special infinite elements ('infinite carriers' with unique characteristics)".
(3) Some elements contained in infinite sets have “infinite law carriers with cognizable quantitative properties (Half Archimedean Property)” related to their unique characteristics, and can be quantitatively understood and studied -------- some infinite sets must contain different quantities of elements; Some elements contained in certain infinite sets do not have “infinite law carriers with cognizable quantitative properties (Half Archimedean Property)” related to their unique characteristics, and it is impossible to carry out any quantitatively cognitions and studies relating to such “infinite law carriers” ------ "infinite" is the unique and identical "quantitative properties" of these elements contained in such infinite sets.