That a bijection exists is incredibly useful. But the idea of "measuring" infinite sets in the cardinality sense is not very interesting or useful.
That a bijection exists is incredibly useful. But the idea of "measuring" infinite sets in the cardinality sense is not very interesting or useful.
Saying that two sets have the same cardinality is equivalent to saying there is a bijection between them. I don't understand how the latter can be useful but not the former?
It isn't very interesting or useful... to you.