You also say an entire paragraph is “simply wrong” but you don’t say what you object to other than to note that the laws concerning finite sets are different than those concerning infinite sets and obviously I agree. But what don’t you like in my statement?
Sniffnoy’s next remark was relevant. What he was saying was simply wrong was the idea that if one set A contains another set B then A must have higher cardinality than B. It seems that you have some confusion about how cardinality of infinite sets behaves. It might help to read the relevant Wikipedia entries starting with the basic one on cardinality or look at a standard textbook on set theory. Some of these issues will also be handled by a real analysis textbook.
Sniffnoy’s next remark was relevant. What he was saying was simply wrong was the idea that if one set A contains another set B then A must have higher cardinality than B. It seems that you have some confusion about how cardinality of infinite sets behaves. It might help to read the relevant Wikipedia entries starting with the basic one on cardinality or look at a standard textbook on set theory. Some of these issues will also be handled by a real analysis textbook.