Nota: A tradução desta entrada está atualmente em revisão de qualidade, portanto parte do conteúdo é exibida temporariamente apenas em inglês.
Este verbete ainda não foi traduzido para o seu idioma, portanto o original é exibido abaixo.
denumerable
This term is used almost exclusively within the context of set theory and higher mathematics. It describes a set that is either finite or countably infinite, meaning its elements can be listed one by one (even if the list goes on forever) such that every element is eventually reached.
In a professional mathematical register, "denumerable" is often used interchangeably with "countable." However, some authors use "denumerable" specifically to refer to sets that are countably infinite, while using "countable" to include both finite and countably infinite sets. It is crucial to check the specific definitions used in a given textbook or paper to avoid ambiguity.
It stands in direct opposition to "uncountable" (or non-denumerable), which describes sets like the real numbers that are too large to be put into a sequence, regardless of how much time is spent counting. Using this word in a casual, non-academic conversation would be perceived as overly formal or pedantic.
Meanings
Examples
Is the set of rational numbers denumerable or uncountable?
Is the set of rational numbers denumerable or uncountable?
I need to prove that this specific subset is denumerable.
A set is denumerable if it can be put into a one-to-one correspondence with the natural numbers.
Wait, if the union of two denumerable sets is also denumerable, then this should work.
The professor explained why the set of algebraic numbers is denumerable.
It seems counterintuitive that the rationals are denumerable given how dense they are.