The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate.
For example, a vector space can have a vector basis which spans the vector space by finite linear combinations.
See also
Basis Point, Change of Basis, Hamel Basis, Hilbert Basis, Orthonormal Basis, Schauder Basis, Standard Basis, Topological Basis, Vector Basis
This entry contributed by Todd Rowland
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Rowland, Todd. "Basis." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Basis.html