Because "the first generation of infinite set theory" (Cantor’s set theory) is based on present classical infinite theory system, it is bound to be unable to get rid of the confusion of "potential infinite and actual infinite" contents, and people have to take the quantity of elements in an infinite set as the mixed number forms of "potential infinite number and actual infinite number" derived from those concepts of "potential infinite and actual infinite". This inevitably leads to two contradictory cognitive behaviors: On the one hand people deny the necessary relationship between "element” and “set" (not knowing at all that the existence of "elements with different properties" leads to the existence of different infinite sets?), firmly deny the characteristic differences of elements contained in different infinite sets (the unique existing meaning, unique existing form and unique existing condition as well as unique relationship between), and construct a kind of “cardinal number theory” by "double abstraction" which is conflict with the nature of infinite set. Through the "double abstraction", elements contained in many infinite sets are turned into piles of “geometric points" without any differences of “unique existing meaning, unique existing form and unique existing condition as well as unique relationship between”, to ensure that they all have the same "cardinal number" (to ensure many different infinite sets have the same quantity of elements). After "double abstraction", elements contained in different infinite sets have lost their original unique properties (including the property of number) and become "endless infinite geometric point"--------"endless" becomes the only numerical property for all the elements contained in many infinite sets (as we know, all the points on the lines are just piles of "endless abstract things" without any differences of “unique existing meaning, unique existing form, unique numerical property and unique existing condition as well as unique relationship between”. All the points on the line segments are with the same "cardinal number" and heir quantities are uniformly "infinite"). So, in present classical set theory (Cantor’s set theory), after "double abstraction", many subsets and their original sets contain same amount of elements -------- the elements contained in many infinite sets have the same "cardinal number" and "endless" becomes the only numerical property for all the elements contained in many infinite sets. On the other hand, all in a sudden, people recognized the necessary relationship between "elements and sets", firmly recognized the importance of the essential differences in the manifestation, nature, existing conditions and relationship among the elements in infinite sets, recognized that it is the existence of "elements with different characteristics" that leads to the existence of different infinite sets; all in a sudden, people denied the "double abstraction theory”, suddenly decided not to apply "double abstraction theory” in the cognitive process for elements contained in the infinite set, so as to ensure the applying of T = {x|x📷x}theory which has nothing to do with "double abstracted” to find some elements still with their special original features (not being "double abstracted”) and to complete some proofs that some infinite sets contain more infinite elements than other sets (for example, the infinite elements contained in Real Number Set are more than the infinite elements contained in Natural Number Set, the infinite elements contained in any infinite set are less than the infinite elements contained in its power set -------- Infinite Real Number Set is more infinite than Infinite Natural Set Number Set, and any infinite set is less infinite than its power set,... For hundreds of years, people have been trying so hard to study and fabricate various "infinite concepts", various formal logic, formal languages and "assembly line" operations related to those "contradictory and colorful concepts of infinite". However, the fundamental defects revealed by these two problems have determined the impossibility of scientific, effective and systematic qualitative and quantitative studies to elements contained in infinite sets, paradoxes are inevitably produced -------- because it is impossible to know at all what the infinite related elements contained in infinite sets are (the abstract things that are both potential infinite and actual infinite: the "ghost" disappearing and reappearing at any time?). Therefore, we draw an important conclusion: "the third mathematical crisis" is another manifestation of "the second mathematical crisis" in set theory. They are "twins". Studies have shown that, the unavoidable conceptual confusion of "potential infinite, actual infinite" in present classical infinite theory system determines Cantor's theory and operations of “cardinal number” and "double abstraction" are not self-justification at all and lack of scientific and systematic, which inevitably results in the impossibility of scientific, effective and systematic qualitative and quantitative studies to elements contained in infinite sets.