# denumerable

Syllabification: de·nu·mer·a·ble
Pronunciation: /dēˈn(y)o͞omərəb(ə)l /

## Definition of denumerable in English:

Mathematics
Able to be counted by a one-to-one correspondence with the infinite set of integers.
Example sentences
• The non-denumerable infinity of real numbers (and thus of points in space and of events in time) is much larger than the merely denumerable infinity of integers.
• The paper discusses denumerable sets, i.e. those which are in 1-1 correspondence with the natural numbers.

### Origin

early 20th century: from late Latin denumerare 'count out' + -able.

### Derivatives

#### denumerability

1
Pronunciation: /-ˌn(y)o͞omərəˈbilitē/
noun
Example sentences
• At least five mathematicians tried to prove denumerability of the value set, to which the names of two of them are attached.
• I don't know how to approach it… but know that it is based on the concept of denumerability of real numbers.
• Combining with his proof of the denumerability of rational numbers, it proves the existence of irrational numbers without actually constructing any irrational number.

#### denumerably

2
Example sentences
• The most famous was his diagonal argument which seems to show that there must be orders of infinity, and specifically that the non-denumerably infinite is distinct from the denumerably infinite.
• This amounts to saying the transfinite whole is not equal to the sum of its denumerably infinite parts.
• This way of reasoning is also present in finite and denumerably infinite collections.

## Definition of denumerable in:

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= trending

## More on denumerable

### More words in this category

arithmetic progression combinatorics commensurable constructivism ctn.
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