ba·sis

[bey-sis]
noun, plural ba·ses [bey-seez] .
1.
the bottom or base of anything; the part on which something stands or rests.
2.
anything upon which something is based; fundamental principle; groundwork.
3.
the principal constituent; fundamental ingredient.
4.
a basic fact, amount, standard, etc., used in making computations, reaching conclusions, or the like: The nurse is paid on an hourly basis. He was chosen on the basis of his college grades.
5.
Mathematics. a set of linearly independent elements of a given vector space having the property that every element of the space can be written as a linear combination of the elements of the set.
Origin:
1525–35; < Latin < Greek básis step, place one stands on, pedestal, equivalent to ba-, base of baínein to walk, step (akin to come) + -sis -sis; cf. base1

Synonyms
1, 2. See base1.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2013.
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00:10
basis is always a great word to know.
So is inverse. Does it mean:
the second power of a quantity, expressed as a2 = a ? a, where a is the quantity
a proportion containing terms of which an increase in one results in a decrease in another
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Collins
World English Dictionary
basis (ˈbeɪsɪs) [Click for IPA pronunciation guide]
 
—n , pl -ses
1.  something that underlies, supports, or is essential to something else, esp an abstract idea
2.  a principle on which something depends or from which something has issued
3.  maths (of a vector space) a maximal set of linearly independent vectors, in terms of which all the elements of the space are uniquely expressible, and the number of which is the dimension of the space: the vectors x, y and z form a basis of the 3-dimensional space all members of which can be written as ax + by + cz
 
[C14: via Latin from Greek: step, from bainein to step, go]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Etymonline
Word Origin & History

basis
1570s, from L. basis "foundation," from Gk. basis "a step, stand, base, that whereon one stands," from bainein "go, step" (see come).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Medical Dictionary

basis ba·sis (bā'sĭs)
n. pl. ba·ses (-sēz')
The foundation upon which something, such as an anatomical part, rests.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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American Heritage
Science Dictionary
basis   (bā'sĭs)  Pronunciation Key 
Plural bases (bā'sēz')
A set of independent vectors whose linear combinations define a vector space, such as a reference frame used to establish a coordinate system.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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American Heritage
Idioms & Phrases

basis

see on a first-name basis.

The American Heritage® Dictionary of Idioms by Christine Ammer.
Copyright © 1997. Published by Houghton Mifflin.
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Example sentences
While there is some basis for this belief, it is certainly an
  oversimplification.
On this basis he built up a philosophy which is usually regarded as the
  foundation of modern thought.
She will assume her new duties on a part-time basis immediately, as she
  completes previous freelance commitments.
Let's go off the scale of tested knowledge and operate purely on the basis of
  mathematics.
Idioms & Phrases
on a first-name basis
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