denumerable
/dɪˈnjuːm(ə)rəb(ə)l
/adjective Mathematics
Able to be counted by a one-to-one correspondence with the infinite set of integers.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.
Derivatives
denumerability
- 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
- 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.
Origin
Early 20th century: from late Latin denumerare 'count out' + -able.