Abstract
We have the sequence , where a norm space. We have a dual space too is the collection of linier and continous functional from norm space into riil number system . If for all the sequence convergent to and then convergent to . The converse of this implication is not applicable . This study aims to explain the properties that apply to the ranks of the weak convergent and explain the relationship between the strong convergent sequence and the weak convergent sequence. From several reference sources then through the review process obtained weak nature of singularity limit sequence and relationship between the strong convergent sequence and the weak convergent sequence that if the sequence is strong convergent therefore the sequence it weak convergent.
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