DENUMERABLE Meaning and
Definition
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Denumerable is an adjective used in mathematics to describe a set that can be associated with the set of natural numbers or is countable. It refers to a set with a one-to-one correspondence to the positive integers and can be enumerated or listed in a systematic and exhaustive manner. Denumerable sets are also known as countable or enumerable sets.
A set is considered denumerable if its elements can be assigned unique natural numbers, starting from 1 and continuing indefinitely. In other words, a set is denumerable if its elements can be counted, labeled or put in a sequence without missing any element. The key characteristic of denumerability is that each element of the set can be reached by counting a specific number of elements from the beginning.
Denumerable sets can include various mathematical objects, such as integers, rational numbers, or even infinite sets such as the set of all positive even numbers. However, not all sets are denumerable. For instance, the set of all real numbers between 0 and 1 (inclusive) is an example of an undenumerable or uncountable set. It cannot be put in a one-to-one correspondence with the natural numbers, as it has a higher cardinality or greater number of elements than the denumerable sets.
The concept of denumerability plays a crucial role in various branches of mathematics, including set theory, analysis, and discrete mathematics. It provides a foundation for understanding the size and cardinality of different sets within the realm of mathematics.
Common Misspellings for DENUMERABLE
- senumerable
- xenumerable
- cenumerable
- fenumerable
- renumerable
- eenumerable
- dwnumerable
- dsnumerable
- ddnumerable
- drnumerable
- d4numerable
- d3numerable
- debumerable
- demumerable
- dejumerable
- dehumerable
- denymerable
- denhmerable
- denjmerable
Etymology of DENUMERABLE
The word denumerable is formed by adding the prefix de- meaning undo or remove to the word numerable. Numerable comes from the Latin word numerabilis, which is derived from numerare meaning to count or number. So, denumerable essentially means not countable or not able to be numbered.
Similar spelling words for DENUMERABLE
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