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> This is neither true nor false as it has no meaning. Whether countable or not, infinite sets do not have sizes to compare. Infinite sets do have cardinality,
by chimeracoder 5y ago
> This is neither true nor false as it has no meaning. Whether countable or not, infinite sets do not have sizes to compare.
Infinite sets do have cardinality, and cardinalities can be compared, in a manner which corresponds pretty well to what people mean when they colloquially say "more" or "fewer".
If you want to split hairs between "size" and "cardinality", that's your choice, but even Cantor himself used the term "size" in this manner.
- shannifin 5y ago> in a manner which corresponds pretty well to what people mean when they colloquially say "more" or "fewer" I would argue that it does not correspond very well to what people mean when they say "more" or "fewer", and hence the apparent paradox of Hilbert's Hotel. That is, my original point was that thinking of infinite sets as having comparable sizes is the precise confusion that leads to the supposed paradox. If you're specifically comparing cardinalities, "more" or "fewer" lose their "colloquial" meaning.