sentences:  The basis problem was posed by Stefan Banach in his book, "Theory of Linear Operators".Banach asked whether every separable Banach space has a Schauder basis.A Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that for Hamel bases we use linear combinations that are "finite" sums, while for Schauder bases they may be "infinite" sums.