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Because of this, languages with gender distinction can often use pronouns where in English a noun would have to be repeated in order to avoid confusion
from the top result below
https://en.wikipedia.org/wiki/Grammatical_gender
Because of this, languages with gender distinction can often use pronouns where in English a noun would have to be repeated in order to avoid confusion
https://en.wikipedia.org/wiki/Financial_economics
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https://en.wikipedia.org/wiki/Outline_of_finance
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https://en.wikipedia.org/wiki/Search_engine
For a search provider, its engine is part of a distributed computing system that can encompass many data centers throughout the world
https://en.wikipedia.org/wiki/Web_search_engine
For a search provider, its engine is part of a distributed computing system that can encompass many data centers throughout the world
https://en.wikipedia.org/wiki/Ideal_norm
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https://en.wikipedia.org/wiki/Up_to
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https://en.wikipedia.org/wiki/Wedderburn%E2%80%93Artin_theorem
}
Here we used right modules because R ≅ E n d ( R R ) {\displaystyle R\cong \mathrm {End} (R_{R})} ; if we used left modules R {\displaystyle R} would be isomorphic to the opposite algebra of E n d ( R R ) {\displaystyle \mathrm {End} ({}_{R}R)} , but the proof would still go through
https://en.wikipedia.org/wiki/Module_homomorphism
Note: the above verification would "fail" if one used the left R-action in place of the right S-action
https://en.wikipedia.org/wiki/Euclidean_division
This can be confirmed using multiplication, the inverse of division: if each of the 4 people received 2 slices, then 4 × 2 = 8 slices were given out in total
https://en.wikipedia.org/wiki/Double_centralizer_theorem
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https://en.wikipedia.org/wiki/Conjugate_diameters
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https://en.wikipedia.org/wiki/Invariant_basis_number
Assuming the ultrafilter lemma (a strictly weaker form of the axiom of choice), this result is actually equivalent to the definition given here, and can be taken as an alternative definition
https://en.wikipedia.org/wiki/Theory_of_knots
Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R 3 {\displaystyle \mathbb {R} ^{3}} upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself
https://en.wikipedia.org/wiki/Bali_myna
[1]
In 2018, there were three locations on Bali where the birds existed in the wild: the West Bali National Park; Bali's small island of Nusa Penida and Begawan Foundation's breeding and release site at Melinggih Kelod, Payangan
https://en.wikipedia.org/wiki/Formal_power_series_ring
} If we studied this as a power series, its properties would include, for example, that its radius of convergence is 1 by the Cauchy–Hadamard theorem
https://en.wikipedia.org/wiki/Glossary_of_nautical_terms_(A%E2%80%93L)
Pirates would often hide their crews below decks, thereby creating the false impression that an encounter with another ship was a casual matter of chance rather than a planned assault
https://en.wikipedia.org/wiki/Glossary_of_nautical_terms_(A-L)
Pirates would often hide their crews below decks, thereby creating the false impression that an encounter with another ship was a casual matter of chance rather than a planned assault
https://en.wikipedia.org/wiki/Nakayama's_lemma
Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle in some sense
https://en.wikipedia.org/wiki/Prime_ideal
This generalizes the following property of prime numbers, known as Euclid's lemma: if p is a prime number and if p divides a product ab of two integers, then p divides a or p divides b
https://en.wikipedia.org/wiki/Basis_(linear_algebra)
: bases) if every element of V can be written in a unique way as a finite linear combination of elements of B
https://en.wikipedia.org/wiki/Outline_of_category_theory
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https://en.wikipedia.org/wiki/Krull's_theorem
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https://en.wikipedia.org/wiki/Projective_dimension
Various equivalent characterizations of these modules appear below
https://en.wikipedia.org/wiki/Commutator_(ring_theory)
[1]
This element is equal to the group's identity if and only if g and h commute (that is, if and only if gh = hg)
https://en.wikipedia.org/wiki/Non-associative_ring
That is, an algebraic structure A is a non-associative algebra over a field K if it is a vector space over K and is equipped with a K-bilinear binary multiplication operation A × A → A which may or may not be associative
https://en.wikipedia.org/wiki/Interval_(mathematics)
(This interval can also be denoted by ] 0 , 1 [ {\displaystyle ]0,1[} , see below)
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem
[3][4]
In simple terms, it states that if a system has a finite volume (or total probability measure) and preserves that volume over time, then almost every initial state will eventually return arbitrarily close to its starting position, and it will do so infinitely many times
https://en.wikipedia.org/wiki/Consistent_estimator
If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent
https://en.wikipedia.org/wiki/Excess_kurtosis
Different measures of kurtosis can yield varying interpretations