basis

Plural: baseis, bases, basises

Noun

• The underlying support or foundation for an idea or argument.
• a relation that provides the foundation for something
  • "he worked on an interim basis"
• the fundamental assumptions from which something is begun or developed or calculated or explained
  • "the whole argument rested on a basis of conjecture"
• the most important or necessary part of something
  • "the basis of this drink is orange juice"
• A physical base or foundation.
• A starting point, base or foundation for an argument or hypothesis.
• An underlying condition or circumstance.
• A regular frequency.
• 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.
• In a vector space, a linearly independent set of vectors spanning the whole vector space.
• Amount paid for an investment, including commissions and other expenses.
• 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.

Examples

• Cars must be checked on a yearly basis.
• Included in the basis could be elevation, cleaning, freight by truck and/or rail, government inspection fees, administration fees, interest and storage charges as well as allowance for risk and profit for the grain dealer.
• Knowing obscure words is the basis of my Scrabble success.
• The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.
• The flights to Fiji leave on a weekly basis.
• You should brush your teeth on a daily basis at minimum.

Synonyms

base, cornerstone, footing, foundation, fundament, ground, groundwork