> just kinda bugs me that the way the formal cardinality of infinite sets is communicated is as the commonsense notion of "size".
It's not in any place doing maths sensibly.
It's just that both the USA and the UK have a terribly unrigorous way of teaching maths even at university level.
If you take a look at the French Wikipedia article on cardinality, you will see that the world size is never used and the closest thing you will find to it is that cardinality can intuitively be seen as the "number" of elements in a set with actual quotes around. The article then compare multiple very rigorous definitions. I expect a translation of it would be unreadable by most American however. The average French reader will have been exposed to significantly more formal mathematics.
Using the world "size" when talking about infinities is just sloppy.
It's not in any place doing maths sensibly.
It's just that both the USA and the UK have a terribly unrigorous way of teaching maths even at university level.
If you take a look at the French Wikipedia article on cardinality, you will see that the world size is never used and the closest thing you will find to it is that cardinality can intuitively be seen as the "number" of elements in a set with actual quotes around. The article then compare multiple very rigorous definitions. I expect a translation of it would be unreadable by most American however. The average French reader will have been exposed to significantly more formal mathematics.
Using the world "size" when talking about infinities is just sloppy.