# basis

Pronunciation: say "BAY-sis" /ˈbeɪ.sɪs/

## Noun

1. The facts, ideas or conditions on which something is based or from which it develops.
   - Simple: The main facts or ideas that something comes from or depends on.
   - _The lawyer built her entire case on the basis of a single witness._
   - _Several recent studies provide the basis for these recommendations._
2. How often something happens or is done, such as daily, weekly or irregularly; usually in the phrase on a … basis.
   - Simple: How often something happens, such as every day or every week.
   - _The team meets on a regular basis to review its progress._
   - _Volunteers are rotated through the shelter on a monthly basis._
3. The terms or arrangement on which something is done or organized, such as part-time, temporary or unpaid work; usually in the phrase on a … basis.
   - Simple: The way something is set up or agreed, for example as part-time or unpaid work.
   - _Most of the museum's guides serve on a voluntary basis._
   - _Tickets will be given out on a first-come, first-served basis._
4. A physical base or foundation on which a structure rests.
   - Simple: The solid part at the bottom that holds something up.
5. In finance and tax, the total cost of acquiring an investment, counting commissions and other expenses as well as the price.
   - Simple: The total money you paid for an investment, including any fees.
   - _The investor's basis in the property included the purchase price and closing costs._
   - _Capital gains are found by subtracting the basis from the final sale price._
6. In a vector space, a set of linearly independent vectors that together span the entire space.
   - Simple: In math, a smallest set of directions you can combine to reach any point in a space.
   - _Any vector in the plane can be written using a basis of two independent vectors._
   - _Changing the basis can greatly simplify the equations describing a transformation._

## Other meanings

- (noun) In commodity trading, the difference between the local cash price paid for a crop and the reference price, usually the futures price for that crop on an exchange.
- (noun) In topology, a collection of subsets of a set that covers the set and, for any two members sharing a point, contains a third member inside their overlap that also holds that point.

## Origin

The root is Proto-Indo-European *gʷem- (which also gives 'come'); from it was derived *gʷémtis, which became Ancient Greek βάσις (básis) and then Latin basis, the source of the English word. It is a doublet of base.

Source: DictionaryAI, https://dictionaryai.com/define/basis (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).