Assertion: sequence | /r/HasProperty | bounded
Facets:
value: likewise
type: DEGREE
Source sentences:
text: If the sequence of real numbers (a n ) is such that all the terms are less than some real number M, then the sequence is said to be bounded from above.
text: A sequence having a lower bound and an upper bound is called the bounded sequence.
text: Likewise, if, for some real m, a n ≥ m for all n greater than some N, then the sequence is bounded from below and any such m is called a lower bound.
text: If a sequence is both bounded from above and bounded from below, then the sequence is said to be bounded.
text: If a sequence is both bounded from above and bounded from below, then the sequence is said to be bounded.
text: If then If a sequence is bounded and monotonic then it is convergent.
text: then If a sequence is bounded and monotonic then it is convergent.
text: We will also determine a sequence is bounded below, bounded above and/or bounded.
text: If there exists a number \(m\) such that \(m \le {a_n}\) for every \(n\) we say the sequence is bounded below.
text: If there exists a number \(M\) such that \({a_n} \le M\) for every \(n\) we say the sequence is bounded above.
text: If the sequence is both bounded below and bounded above we call the sequence bounded.
text: A sequence is bounded below if we can find any number \(m\) such that \(m \le {a_n}\) for every \(n\).
text: In other words, there are an infinite number of lower bounds for a sequence that is bounded below, some will be better than others.
text: Also, since the sequence terms will be either zero or negative this sequence is bounded above.
text: Therefore, while the sequence is bounded above it is not bounded.
text: The sequence is bounded however since it is bounded above by 1 and bounded below by -1.
text: Therefore, this sequence is bounded.
text: So, this sequence is bounded.
text: First, notice that, as with the previous part, the sequence terms are all positive and will all be less than one (since the numerator is guaranteed to be less than the denominator) and so the sequence is bounded.
text: The sequence is bounded.