BASIS

basis, base, foundation, fundament, groundwork, cornerstone

(noun) the fundamental assumptions from which something is begun or developed or calculated or explained; “the whole argument rested on a basis of conjecture”

footing, basis, ground

(noun) a relation that provides the foundation for something; “they were on a friendly footing”; “he worked on an interim basis”

basis, base

(noun) the most important or necessary part of something; “the basis of this drink is orange juice”

Source: WordNet® 3.1

Etymology

Noun

basis (plural bases or baseis or basises)

A physical base or foundation.

A starting point, base or foundation for an argument or hypothesis.

An underlying condition or circumstance.

A regular frequency.

(linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.

(accounting) Amount paid for an investment, including commissions and other expenses.

(topology) 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.