bounded sequence
[ˈbaʊndɪd ˈsiːkwəns]
nounpl: bounded sequences
sequência limitada
1. A sequence of numbers where all terms are contained within a fixed range; mathematically, a sequence {aₙ} is bounded if there exist real numbers m and M such that m ≤ aₙ ≤ M for all n
The sequence {1/n} is a bounded sequence because all its terms lie between 0 and 1.
A sequência {1/n} é uma sequência limitada porque todos os seus termos estão entre 0 e 1.
2. In mathematical analysis, a sequence whose terms do not approach infinity in absolute value
The bounded sequence sin(n) oscillates but remains between -1 and 1 for all values of n.
A sequência limitada sin(n) oscila mas permanece entre -1 e 1 para todos os valores de n.
This is a fundamental concept in mathematical analysis taught in both Brazilian and American higher education. The term is used identically across English-speaking and Portuguese-speaking academic communities. Understanding bounded sequences is essential for studying calculus, real analysis, and topology.
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