basis
Pronunciation Noun

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.
    • 2013, Daniel Taylor, Danny Welbeck leads England's rout of Moldova but hit by Ukraine ban (in The Guardian, 6 September 2013)
      Hodgson may now have to bring in James Milner on the left and, on that basis, a certain amount of gloss was taken off a night on which Welbeck scored twice but barely celebrated either before leaving the pitch angrily complaining to the Slovakian referee.
  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. (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
  6. (accounting) Amount paid for an investment, including commissions and other expenses.
  7. (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.
Synonyms
  • (starting point for discussion) base
Translations Translations Translations Translations


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