countable groups

[ˈkaʊntəbəl ɡruːps]
nounpl: countable groups
grupos contáveis
1. In mathematics, particularly in algebra and group theory, groups whose elements can be enumerated in a sequence (finite or infinite but bijective with natural numbers)
The additive group of integers is one of the simplest examples of countable groups.
O grupo aditivo dos inteiros é um dos exemplos mais simples de grupos contáveis.
2. Groups with cardinality equal to that of the natural numbers (aleph-null)
Most finitely generated groups are countable groups.
A maioria dos grupos finitamente gerados são grupos contáveis.
This is specialized mathematical terminology used primarily in academic and research contexts. The concept is foundational in abstract algebra and is taught in upper-level undergraduate and graduate mathematics courses in both Brazil and the United States. There is no significant cultural variation in usage; the term maintains consistent meaning across Portuguese-speaking and English-speaking mathematical communities.
Synonyms / Sinônimos
enumerable groupsdiscrete countable groupsdenumerably infinite groups
Antonyms / Antônimos
uncountable groupsnon-enumerable groupscontinuous groups

Regional Variations

General Brazilian Portuguese
grupos contáveis
Standard mathematical terminology used in Brazilian universities and textbooks
European Portuguese
grupos contáveis
Same terminology, used in Portuguese academic mathematics literature
Academic English (USA)
countable groups
Standard term in American mathematical texts and journals

Related Words

group theorycardinalityfinite groupsinfinite groupsenumerable setsdiscrete mathematics
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