Adjective
/dɪˈnjuː.mə.rə.bəl/
The term "denumerable" refers to a set that can be counted or listed out, typically in the context of mathematics and set theory. It is synonymous with "countable," meaning that there exists a one-to-one correspondence between the members of the set and the natural numbers. The term is more frequently used in written contexts, particularly in academic and mathematical discussions, than in oral speech.
The set of natural numbers is denumerable, as each number can be matched with a unique natural number.
Translation: El conjunto de números naturales es denumerable, ya que cada número puede ser emparejado con un número natural único.
Mathematicians often study denumerable sets to understand the properties of infinite collections.
Translation: Los matemáticos a menudo estudian conjuntos denumerables para entender las propiedades de las colecciones infinitas.
A denumerable infinity is smaller than a continuum in set theory.
Translation: Una infinitud denumerable es más pequeña que un continuo en teoría de conjuntos.
While "denumerable" may not form many idiomatic expressions, it often appears in the context of mathematical terminology. Here are a few related expressions:
Denumerable infinity: Refers to the concept of an infinite set that can be listed out, such as the integers.
Translation: La infinitud denumerable se refiere al concepto de un conjunto infinito que puede ser listado, como los enteros.
Denumerable set: This term is a standard phrase in mathematics indicating a set that can be counted.
Translation: El conjunto denumerable es una frase estándar en matemáticas que indica un conjunto que puede ser contado.
Countably infinite: This is another way of expressing the idea of denumerable sets in a less formal context.
Translation: Infinitamente contable es otra manera de expresar la idea de conjuntos denumerables en un contexto menos formal.
The word "denumerable" derives from the Latin "denumerare," which means "to enumerate" or "to count." It combines the prefix "de-" (indicating reversal or removal) with "numerable," which stems from "numerus," the Latin word for "number."
Synonyms: - Countable - Enumerated - Finite (in specific contexts)
Antonyms: - Uncountable - Non-denumerable - Infinite (in certain contexts)
This comprehensive breakdown of the term "denumerable" provides clarity on its mathematical and linguistic significance, along with relevant examples and expressions in context.