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The number of elements of a pid may be finite or countably infinite...or infinite also....but a finite field is always a pid
No, it is countably infinite.
There are finite sets, countably infinite sets and uncountably infinite sets.
No. The set of irrational numbers has the same cardinality as the set of real numbers, and so is uncountable.The set of rational numbers is countably infinite.
Yes, there are countably infinite rationals but uncountably infinite irrationals.
One possible classification is finite, countably infinite and uncountably infinite.
Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.
Closed sets and open sets, or finite and infinite sets.
Yes, because it is countably infinite.
An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite.
An infinite number. (Countably infinite, if you want to be more precise, though perhaps more confusing).
Finite, countably infinite and uncountably infinite.