Assertion: sequence | /r/HasProperty | convergent
Facets:
value: strongly
type: DEGREE
value: in ℓ1
type: LOCATION
value: weakly
type: DEGREE
Source sentences:
text: If then If a sequence is bounded and monotonic then it is convergent.
text: If such a limit exists, the sequence is called convergent.
text: A sequence is convergent if and only if all of its subsequences are convergent.
text: The space ℓ1 has the Schur property: In ℓ1, any sequence that is weakly convergent is also strongly convergent (Schur 1921).
text: The space ℓ1 has the Schur property: In ℓ1, any sequence that is weakly convergent is also strongly convergent (Schur 1921).
text: then If a sequence is bounded and monotonic then it is convergent.
text: A sequence is convergent if and only if every subsequence is convergent.
text: A sequence is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259).
text: If it does, we say that the sequence is convergent and has a limit equal to L.
text: A sequence is convergent if there exists a number L such that the numbers get closer and closer to L as n gets larger.