basis

noun

1. A physical base or foundation.
2. A starting point, base or foundation for an argument or hypothesis.
3. An underlying condition or circumstance.
4. A regular frequency.
5. The difference between the cash price a dealer pays to a farmer for his produce and an agreed reference price, which is usually the futures price at which the given crop is trading at a commodity exchange.
6. In a vector space, a linearly independent set of vectors spanning the whole vector space.
7. Amount paid for an investment, including commissions and other expenses.
8. A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.