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countability
This term is primarily used as a technical descriptor across three distinct fields: general logic, linguistics, and mathematics. In general usage, it refers to the simple possibility of enumeration. In linguistics, it describes a grammatical category that dictates how a noun interacts with determiners and number markers, distinguishing between discrete units and mass substances.
In the context of set theory, the term takes on a highly specialized meaning regarding cardinality. Here, it does not merely mean "can be counted" in a finite sense, but refers to sets that can be put into a one-to-one correspondence with the set of natural numbers, including countably infinite sets.
Meanings
Examples
The countability of the stars in this small cluster makes them easy to map.
I wonder if the countability of these grains of sand is even possible.
The professor explained the countability of nouns during the grammar lecture.
Does this noun have countability or is it strictly an uncountable mass noun?
Some words shift their countability depending on the context of the sentence.
We must first establish the countability of the set before proceeding with the proof.
The countability of the rational numbers is a fundamental concept in set theory.
He struggled to grasp the difference between countability and uncountability in infinite sets.