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.

When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak König's lemma, with the equivalence provable in RCA < sub > 0 </ sub > ( a second-order variant of Peano arithmetic restricted to induction over Σ < sup > 0 </ sup >< sub style =" margin-left :- 0. 6em "> 1 </ sub > formulas ).

S is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, total, trichotomous, a partial order, total order, strict weak order, total preorder ( weak order ), an equivalence relation, or a relation with any other special properties, if and only if R is.

* Define a b as " not b < a " ( i. e., take the inverse complement of the relation ), which corresponds to defining a ~ b as " neither a < b nor b < a "; these relations and ~ are in general not transitive ; however, if they are, ~ is an equivalence ; in that case "<" is a strict weak order.

* The relation is a strict weak order, where the associated equivalence is equality.

If one reagent is a weak acid or base and the other is a strong acid or base, the titration curve is irregular and the pH shifts less with small additions of titrant near the equivalence point.

Titration curves corresponding to weak bases and strong acids are similarly behaved, with the solution being acidic at the equivalence point and indicators such as methyl orange and bromothymol blue being most appropriate.

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.

* The weak equivalence principle: The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.

They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms ( e. g., a weak equivalence of spaces passes to an isomorphism of homology groups ), verified that all existing ( co ) homology theories satisfied these axioms, and then proved that such an axiomatization uniquely characterized the theory.

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 >).

* 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

* 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

* Strict weak ordering – a strict partial order in which incomparability is an equivalence relation

Certain axioms, such as stability of fibrations under composition and pullbacks, factorization of every morphism into the composition of an acyclic cofibration followed by a fibration or a cofibration followed by an acyclic fibration, where the word " acyclic " indicates that the corresponding arrow is also a weak equivalence, and other requirements are set up to allow the abstract treatment of homotopy theory.

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

Due to this circumstance, a functor with these properties is sometimes called a weak equivalence of categories ( unfortunately this conflicts with terminology from homotopy theory ).

One may therefore view an adjointness relation between two functors as a " very weak form of equivalence ".

Critics of the SAP argue in favor of a weak anthropic principle ( WAP ) similar to the one defined by Brandon Carter, which states that the universe's ostensible fine tuning is the result of selection bias: i. e., only in a universe capable of eventually supporting life will there be living beings capable of observing any such fine tuning, while a universe less compatible with life will go unbeheld.

The anthropic principle is often criticized for lacking falsifiability and therefore critics of the anthropic principle may point out that the anthropic principle is a non-scientific concept, even though the weak anthropic principle, " conditions that are observed in the universe must allow the observer to exist ", is " easy " to support in mathematics and philosophy, i. e. it is a tautology or truism

While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU ( 3 ) and SU ( 2 ) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U ( 1 ) which in principle allows for arbitrary charge assignments.

The weak anthropic principle could then be applied to conclude that we ( as conscious beings ) would only exist in one of those few universes that happened to be finely tuned, permitting the existence of life with developed consciousness.

Popularly known as the Sapir – Whorf hypothesis, or Whorfianism, the principle is often defined as having two versions: ( i ) the strong version that language determines thought and that linguistic categories limit and determine cognitive categories and ( ii ) the weak version that linguistic categories and usage influence thought and certain kinds of non-linguistic behaviour.

Also the distinction between a weak and a strong version of the hypothesis is a later invention, as Sapir and Whorf never set up such a dichotomy although in their writings at times their view of this relativity principle are phrased in stronger or weaker terms.

The notion of " weak " and " strong " versions of Whorf's principle of linguistic relativity is a misunderstanding of Whorf promulgated by Stuart Chase, whom Whorf considered " utterly incompetent by training and background to handle such a subject.

* Social Choice and Individual Values for the '( weak ) Pareto principle '

When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, the equilibrium is shifted to the left, in accordance with Le Chatelier's principle.

In that sense the behavior of light in this apparatus is deterministic, but there is no way to predict where in the resulting interference pattern any individual photon will make its contribution ( although, there may be ways to use weak measurement to acquire more information without violating the Uncertainty principle ).

It is said that " aggression has its own value ", meaning that often aggressive plays can make money with weak hands because of bluff value.

Although the doctrine of separation of power plays a role in the United Kingdom's constitutional doctrine, the UK constitution is often described as having " a weak separation of powers " A. V. Dicey, despite its constitution being the one to which Montesquieu originally referred.

This indicates that solar heating, although very weak at Triton's great distance from the Sun, plays a crucial role.

Even though the interaction energy is very weak (~ 10 – 100 meV ), physisorption plays an important role in nature.

) Although he appears at first to be foppish and weak, the doctor later shows himself to be both intelligent and courageous, and he plays an important role in defeating Steerpike.

On basic, current computer chess architecture, GNU Chess plays at senior master / weak international master strength ( 2500 + Elo on simple hardware-Intel Core 2 Duo ), without parallel processing, according to the IQ6 test suite.

Although the vulture plays an important natural role, in the Western world, the image of the vulture is quite negative, with ' vulture ' used as a metaphor for those who prey on the weak or dying, with associated negative connotations of cowardice and selfishness.

Early roles included Fellini's The White Sheik in 1952, Fellini's I vitelloni ( 1953 ), a movie about young slackers, in which he plays a weak, effeminate immature loafer and a starring role in Lo scapolo ( The Bachelor ) playing a single man trying to find love.

Quintile measures of inequality satisfy the transfer principle only in its weak form because any changes in income distribution outside the relevant quintiles are not picked up by this measures ; only the distribution of income between the very rich and the very poor matters while inequality in the middle plays no role.

Her plays feature the chastity and perseverance of Christian women and contrast these to the perceived Latin portrayal of women as weak and emotional.

In Letter 6, Voltaire attacks the Presbyterians, whom he sees as intolerant (" Presbyterian affects a serious gait, puts on a sour look, wears a vastly broad-brimmed hat and a long cloak over a very short coat, preaches through the nose, and gives the name of the whore of Babylon to all churches where the ministers are so fortunate as to enjoy an annual revenue of five or six thousand pounds, and where the people are weak enough to suffer this, and to give them the titles of my lord, your lordship, or your eminence ") and overly strict (" No operas, plays, or concerts are allowed in London on Sundays, and even cards are so expressly forbidden that none but persons of quality, and those we call the genteel, play on that day ; the rest of the nation go either to church, to the tavern, or to see their mistresses ").

Perhaps his greatest influence though is the thought of Friedrich Nietzsche, whose " discovery of the ' lie ', the discovery that alleged ' values ' and metaphysical structures are just a play of forces " ( 1993: 93 ) plays an important role in Vattimo's notion of " weak thought.