enumerable
Definition
- Adjective:
- Capable of being counted; countable: Describes something that can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...) or a subset of them, meaning its elements can be listed in a sequence.
Usage
The adjective "enumerable" is used primarily in formal, technical, or academic contexts, especially in mathematics, computer science, and logic. It describes sets or collections where the items can be systematically listed or counted, even if the total number is infinite (like the set of all integers).
Examples
- Adjective:
- The set of even numbers is enumerable because we can list them as 2, 4, 6, 8, and so on.
- In computer science, a decidable problem often has an enumerable set of solutions.
- Not all infinite sets are enumerable; the set of real numbers is a classic example of a non-enumerable set.
Advanced Usage
- "Recursively enumerable": A key concept in computability theory. A set is recursively enumerable if there exists an algorithm that can list its elements (though it may run forever for an infinite set). It is a more specific type of enumerability.
- The halting problem is defined for recursively enumerable sets.
Variants and Related Words
- Enumerate (verb): To mention items one by one; to list.
- She asked me to enumerate all the reasons for my decision.
- Enumeration (noun): The action of mentioning a number of things one by one; a numbered list.
- The document contained a detailed enumeration of the charges.
Synonyms
- Countable
- Denumerable (often used interchangeably in mathematics, though sometimes "denumerable" specifically means countably infinite).
Antonyms
- Non-enumerable
- Uncountable
- Innumerable (typically means too many to be counted, often used hyperbolically rather than technically)
Adjective
-
that can be counted
-
countable sins
-
numerable assets
-
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