continuous function

[kənˈtɪnjuəs ˈfʌŋkʃən]
nounpl: continuous functions
função contínua
1. In mathematics, a function where small changes in the input produce small changes in the output; a function f is continuous at a point if the limit of f(x) as x approaches that point equals f at that point
The function f(x) = x² is a continuous function over all real numbers.
A função f(x) = x² é uma função contínua em todos os números reais.
2. A function with no breaks, jumps, or discontinuities in its graph
Unlike the floor function, the sine function is continuous everywhere.
Diferentemente da função piso, a função seno é contínua em todos os pontos.
3. In topology, a function between topological spaces where the preimage of every open set is open
In topology, a continuous function preserves the structure of open sets.
Em topologia, uma função contínua preserva a estrutura dos conjuntos abertos.
This is a fundamental concept in mathematics education taught at high school and university levels in both Brazil and Portugal. The term is part of standardized mathematical vocabulary and is identical across Portuguese-speaking regions. In the USA, it is a cornerstone concept in calculus, real analysis, and topology courses.
Synonyms / Sinônimos
continuous mappingcontinuous map
Antonyms / Antônimos
discontinuous functionstep function

Regional Variations

General Brazilian
função contínua
Standard mathematical terminology used in Brazilian universities and textbooks
Portugal
função contínua
Same terminology; identical usage in Portuguese mathematics education
USA/English-speaking
continuous function
Fundamental concept taught in calculus and real analysis courses

Related Words

continuitydiscontinuitylimitdifferentiable functiontopologydomainrange
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