** Graphing calculator screens have a resolution typically less than 120 × 90 pixels, whereas computer monitors typically display 1280x1024 pixels or more.

** In the realm of relativistic many-bodied mechanics, namely the time-symmetric Wheeler – Feynman absorber theory: the equivalence between an advanced Liénard – Wiechert potential of particle j acting on particle i and the corresponding potential for particle i acting on particle j was demonstrated exhaustively to order before being proved mathematically.

** Turing equivalence ( theory of computation )

** Moral equivalence

** Logical equivalence

** Improper rotation equivalence

** Rotational equivalence

** Probabilistic equivalence

** Dynamic and formal equivalence

** Lorentz surface, a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics.

** there is a one-to-one correspondence between outgoing edges of any two nodes of the same information set — thus the set of all outgoing edges of an information set is partitioned in equivalence classes, each class representing a possible choice for a player's move at some point —, and

** Atlas III was a US launch vehicle ( 2000 – 2005 )

** Atlas V ( 2002 – Present )

** Atlas Major, a Standard Motor Company van 1962 – 1963

** The Banach – Tarski paradox.

** The Nielsen – Schreier theorem, that every subgroup of a free group is free.

** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals

** The Banach – Alaoglu theorem about compactness of sets of functionals.

** Every Tychonoff space has a Stone – Čech compactification.

** This is a distinguished work which stands out from, and above, many of the books and articles which have ben written in this century on Avicenna ( Ibn Sīnā ) ( A. D. 980 – 1037 ).

** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.

** Laozi ( 5th – 4th century BC )

** Ge Hong ( 283 AD – 343 AD )

** Xun Zi ( c. 312 BC – 230 BC )

** Gongsun Long ( c. 325 BC – c. 250 BC )

** Zou Yan ( 305 BC – 240 BC )

** Mani ( c. 216 AD – 276 AD )

** Haliotis brazieri f. hargravesi ( Cox, 1869 ) – synonym: Haliotis ethologus, the Mimic abalone, Haliotis hargravesi, the Hargraves ’ s abalone

** Haliotis dalli roberti McLean, 1970 – synonym: Haliotis roberti

** Haliotis diversicolor squamata Reeve, 1846 – synonym: Haliotis squamata – the scaly Australian abalone

** Haliotis diversicolor supertexta – the Taiwan abalone or jiukong

** Haliotis kamtschatkana assimilis Dall, 1878 – synonym: Haliotis assimilis, the threaded abalone

** Haliotis ovina f. patamakanthini Dekker, Regter, & Gras, 2001 – synonym: Haliotis patamakanthini

** Haliotis rubra conicopora Péron, 1816 – synonym: Haliotis conicopora – the conical pore abalone

Kleene's Church – Turing Thesis: A few years later ( 1952 ) Kleene would overtly name, defend, and express the two " theses " and then " identify " them ( show equivalence ) by use of his Theorem XXX:

* Raymond Wilder ( 1965 ) Introduction to the Foundations of Mathematics 2nd edition, Chapter 2-8: Axioms defining equivalence, pp 48 – 50, John Wiley & Sons.

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 ).

( Any theory that includes conservation of energy and mass – energy equivalence must include gravitational redshift.

Dyson is best known for demonstrating in 1949 the equivalence of the formulations of quantum electrodynamics that existed by that time – Richard Feynman's diagrams, on the one hand, and, on the other, the operator method developed by Julian Schwinger and Sin-Itiro Tomonaga.

Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J < sup > PC </ sup >( m ), where J is the spin quantum number, P the intrinsic parity ( or P-parity ), and C, the charge conjugation ( or C-parity ), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks ; rather, due to mass – energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.

For compact groups, the Peter – Weyl theorem explains how one may get harmonics by choosing one irreducible representation out of each equivalence class of representations.

* The electronvolt ( eV ) is primarily a unit of energy, but because of the mass – energy equivalence it can also function as a unit of mass.

* Energy also has mass according to the principle of mass – energy equivalence.

In 1905, Albert Einstein formulated the idea of mass – energy equivalence.

This leads to the mass – energy equivalence formula E = mc².

The excess mass Δm = M – Mp is the invariant mass of the energy that is released as photons ( gamma rays ) and kinetic energy of the fission fragments, according to the mass-energy equivalence formula E = mc < sup > 2 </ sup >.

File: Albert Einstein ( Nobel ). png | Albert Einstein ( 1879-1955 ): revolutionized physics due to his theories of special and general relativity, described Brownian motion, awarded the Nobel Prize in Physics in 1921 for his work on the photoelectric effect, formulated mass – energy equivalence formula E = mc < sup > 2 </ sup >, published more than 300 scientific papers and over 150 non-scientific works, considered the " Father of Modern Physics "

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.

) Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass – energy equivalence formula E = mc < sup > 2 </ sup >, where c is the speed of light in vacuum.

* Mass – energy equivalence:, energy and mass are equivalent and transmutable.

The first three of these characterizations can be proven equivalent in Zermelo – Fraenkel set theory without the axiom of choice, but the equivalence of the third and fourth cannot be proved without additional choice principles.

* 1686 – Isaac Newton uses a fixed length pendulum with weights of varying composition to test the weak equivalence principle to 1 part in 1000

* 1889 – Loránd Eötvös uses a torsion balance to test the weak equivalence principle to 1 part in one billion

* 1907 – Albert Einstein introduces the principle of equivalence of gravitation and inertia and uses it to predict the gravitational redshift

* 1960 – Robert Pound and Glen Rebka test the gravitational redshift predicted by the equivalence principle to approximately 1 %

* 1962 – Robert Dicke, Peter Roll, and R. Krotkov use a torsion fiber balance to test the weak equivalence principle to 2 parts in 100 billion

* 1968 – Kenneth Nordtvedt studies a possible violation of the weak equivalence principle for self-gravitating bodies and proposes a new test of the weak equivalence principle based on observing the relative motion of the Earth and Moon in the Sun's gravitational field