From Latin basis, from Ancient Greek βάσις, from Proto-Indo-European *gʷémtis, derived from Proto-Indo-European *gʷem- (whence also come).

• (RP, America) IPA: /ˈbeɪ.sɪs/,
• (Australia) IPA: /ˈbæɪ.sɪs/

basis

1. A physical base or foundation.
   • 1695, William Congreve, To the King, on the taking of Namur, 1810, Samuel Johnson, Alexander Chalmers (biographies), The Works of the English Poets from Chaucer to Cowper, Volume 10, page 271 ↗,

     Beholding rocks from their firm basis rent;
     Mountain on mountain thrown,
     With threatening hurl, that shook th' aerial firmament!

2. A starting point, base or foundation for an argument or hypothesis.
   • 2019, [https://web.archive.org/web/20190311070055/https://learningenglish.voanews.com/a/south-korea-proposes-rain-project-with-china-to-cut-pollution/4819207.html VOA Learning English] (public domain)

     I wonder if the South Korean side has any basis that its smog is from China.

3. An underlying condition or circumstance.
4. A regular frequency.

   You should brush your teeth on a daily basis at minimum.

   The flights to Fiji leave on a weekly basis.

   Cars must be checked on a yearly basis.

5. (agriculture, trading) 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.
   • 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.https://www.alberta.ca/wheat-basis-levels.aspx
6. (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
7. (accounting) Amount paid for an investment, including commissions and other expenses.
8. (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.

   The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.

• (starting point for discussion) base

• German: Fundament
• Italian: fondamenta
• Russian: основа́ние

• French: base
• German: Basis, Grundlage
• Italian: base
• Portuguese: base, fundamento
• Russian: осно́ва
• Spanish: base, fundamento

• French: base
• German: Basis, Grundlage
• Italian: base
• Portuguese: fundamento
• Russian: ба́за
• Spanish: base, fundamento

• French: base
• German: Basis
• Italian: base
• Portuguese: base
• Russian: ба́зис
• Spanish: base

• Italian: cifra, ammontare, cifra base, ammontare base