: This article is about equivalency in mathematics ; for equivalency in music see equivalence class ( music ).

In these units, both distances and times are expressed in inverse energy units ( while energy and mass are expressed in the same units, see Mass – energy equivalence ).

According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors ( see Eötvös experiment ), there is a universality of free fall ( also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass ): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.

One way to see this equivalence is to " move up " the red nodes in a graphical representation of the red – black tree, so that they align horizontally with their parent black node, by creating together a horizontal cluster.

The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum, and see if they hit the ground at the same time.

Without using countable choice, it is not possible to constructively prove the fundamental theorem of algebra for complex numbers based on the Dedekind real numbers ( which are not constructively equivalent to the Cauchy real numbers without countable choice < ref > For the minimum necessary to prove their equivalence, see Bridges, Schuster, and Richman ; 1998 ; < cite > A weak countable choice principle </ cite >; available from .</ ref >).

Consider the polynomial ring R, and the irreducible polynomial The quotient space is given by the congruence As a result, the elements ( or equivalence classes ) of are of the form where a and b belong to R. To see this, note that since it follows that,,, etc.

There has been significant controversy in the field over the equivalence or otherwise of the two techniques ( see exploratory factor analysis versus principal components analysis ).

A conformal manifold is a differentiable manifold equipped with an equivalence class of ( pseudo -) Riemannian metric tensors, in which two metrics g and h are equivalent ( see also: Conformal equivalence ) if and only if

These equivalent magnetic currents are obtained using equivalence principles which, in the case of an infinite planar interface, allow any electric currents, J to be " imaged away " while the fictitious magnetic currents are obtained from twice the aperture electric field ( see Scott ).

It is straightforward to see that defining the same germ at x is an equivalence relation ( be it on maps or sets ), and the equivalence classes are called germs ( map-germs, or set-germs accordingly ).

Also, ω < sub > 1 </ sub > is the smallest uncountable ordinal ( to see that it exists, consider the set of equivalence classes of well-orderings of the natural numbers ; each such well-ordering defines a countable ordinal, and ω < sub > 1 </ sub > is the order type of that set ), ω < sub > 2 </ sub > is the smallest ordinal whose cardinality is greater than ℵ < sub > 1 </ sub >, and so on, and ω < sub > ω </ sub > is the limit of ω < sub > n </ sub > for natural numbers n ( any limit of cardinals is a cardinal, so this limit is indeed the first cardinal after all the ω < sub > n </ sub >).

Applying it to kernels and cokernels, we see that the equivalence F is an exact functor.

( To see the first inclusion, consider any real number r in 1 and let v be the representative in V for the equivalence class ; then r − v = q for some rational number q in 1.

More generally, in musical set theory partitioning is the division of the domain of pitch class sets into types, such as transpositional type, see equivalence class and cardinality.

When they are put into their line, each prisoner can see what equivalence class the actual sequence of hats belongs to.

The equivalence between the category of connected real Lie groups and finite dimensional real Lie algebras is called usually ( in the literature of the second half of 20th century ) Cartan's or Cartan-Lie theorem as it is proved by Élie Cartan whereas S. Lie has proved earlier just the infinitesimal version ( local solvability of Maurer-Cartan equations ( see Maurer-Cartan form ) or the equivalence between the finite dimensional Lie algebras and the category of local Lie groups ).

The most common complexity class involving advice is P / poly where advice length f ( n ) can be any polynomial in n. P / poly is equal to the class of decision problems such that, for every n, there exists a polynomial size Boolean circuit correctly deciding the problem on all inputs of length n. One direction of the equivalence is easy to see.

* For unitary equivalence of bounded operators in Hilbert space, see self-adjoint operator.

* For unitary equivalence of unitary representations see that page.

For details, see dynamic and formal equivalence.

Let him chafe with impatience to see Charles, rip open the note with trembling hands and read the formal report in Hillman's beautiful, schoolmaster's hand.

To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K.

Typical of his satire and cynical humour, the book included a discourse on Parkinson's Law of Triviality ( debates about expenses for a nuclear plant, a bicycle shed, and refreshments ), a note on why driving on the left side of the road ( see road transport ) is natural, and suggested that the Royal Navy would eventually have more admirals than ships.

" but please note that a linking verb has nothing to do with these so called " Be "- verbs ( see below ).

There is a formula for the derivative of f in terms of the derivative of g. To see this, note that f and g satisfy the formula

To summarize, every established national group used cultural productions to assert and strengthen a sense of national unity and destiny ; less politically consolidated groups, especially those pursuing the goal of nationhood, used them in the same ways, though often with a note of determination that makes them easier to see from our contemporary point of reference.

The effect begins to be seen at partial vacuum pressures of a few torr ( several hundred pascals ), reaches a peak at around 10 < sup >− 2 </ sup > torr ( 1 pascal ) and has disappeared by the time the vacuum reaches 10 < sup >− 6 </ sup > torr ( 10 < sup >− 4 </ sup > pascal ) ( see explanations note 1 ).

Equally, gays and lesbians do not see the Bible as unequivocally true because they are forced by its use against them to read it more closely and with less credulity, leading them to note its myriad contradictions.

For the musical note, see E ♯ ( musical note ).

In Australia, Canada and the United States electrical engineers make up around 0. 25 % of the labor force ( see < span id =" demographics_back "> note </ span >).

* Level A: Consistent Randomised Controlled Clinical Trial, cohort study, all or none ( see note below ), clinical decision rule validated in different populations.

The New York Times described the contents of his two-page suicide note to his wife: " he was heartbroken at being unable to see her once again, and expressing deep regret at having hurt her, the dearest thing in his life.

* aspect — Ancient Greek: imperfective, perfective ( traditionally called aorist ), perfect ( sometimes also called perfective ; see note about terminology );

In the image of the tabulator ( see left ), note the control panel, which is visible on the right side of the tabulator.

To see why this works, note that the polynomial can be written in the form

Encirclement tactics are not unique in warfare ( see Battle of Cannae ), and historians note that attempts to surround an enemy were not unknown even in the ritualised battles.

It is effective at killing a large number of insects, notably bed bugs and head lice ( but note toxicity to humans, see below ).

It caused Escoffier to note when he was asked to write the preface that he could " see with my own eyes ," and " Montagné cannot hide from me the fact that he has used Le Guide as a basis for his new book, and certainly used numerous recipes.

It is perhaps important to note that this is not always a conscious process — generally we don't catalog various similarities until we reach a certain threshold, we just intuitively see the resemblances.

* acute accents ( e. g. á ) on a, e, i, o, u, w, y, A, E, I, O, U, W, Y are generated by pressing the AltGr key together with the letter, or AltGr and apostrophe, followed by the letter ( see note below );

As had been the case since the Ars Nova ( see Medieval music ), there could be either two or three of these for each breve ( a double-whole note ), which may be looked on as equivalent to the modern " measure ," though it was itself a note value and a measure is not.

It is important to note that practicing memory skills such as these does not expand working memory capacity proper: It is the capacity to transfer ( and retrieve ) information from long-term memory that is improved, according to Ericsson and Kintsch ( 1995 ; see also Gobet & Simon, 2000 ).