English- translations for basis

A physical base or foundation
A starting point, base or foundation for an argument or hypothesis
An underlying condition or circumstance
A regular frequency
In a vector space, a linearly independent set of vectors spanning the whole vector space
A collection of subsets 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

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

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