discontinuous function
[/ˌdɪs.kənˈtɪn.ju.əs ˈfʌŋk.ʃən/]
nounpl: discontinuous functions
função descontínua
1. A mathematical function that is not continuous at one or more points in its domain; a function where there exists at least one point where the limit does not equal the function value or where the limit does not exist
The function f(x) = 1/x is a discontinuous function because it has a discontinuity at x = 0.
A função f(x) = 1/x é uma função descontínua porque possui uma descontinuidade em x = 0.
2. A function that has breaks, jumps, or gaps in its graph
The floor function is a discontinuous function with jump discontinuities at every integer value.
A função piso é uma função descontínua com descontinuidades de salto em cada valor inteiro.
This is a technical mathematical term used universally in both English and Portuguese-speaking mathematics education. It is standardized terminology with no significant regional or cultural variations. The concept is fundamental to calculus and real analysis courses taught at the university level in both Brazil and Portugal.
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