Even worse, it could keep radiating infinite amounts of energy because there were infinitely many negative energy states available.

The elementary charge, the charge of a proton ( equivalently, the negative of the charge of an electron ), is approximately .< ref name = CODATA > The inverse value ( the number of elementary charges in 1C ) is given by 1 / = 6. 24150965 ( 16 )× 10 < sup > 18 </ sup >.</ ref > In SI, the elementary charge in coulombs is an approximate value: no experiment can be infinitely accurate.

This was then disproved by Haselgrove in 1958 ( see the reference below ), who showed that T ( n ) takes negative values infinitely often.

By convention, the reference location is usually taken at infinity, so the gravitational potential is zero infinitely far away from any mass and negative at any finite distance.

the negative binomial distribution, and the Gamma distribution are examples of infinitely divisible distributions — as are the normal distribution, Cauchy distribution and all other members of the stable distribution family.

Recall that a conditionally convergent series of real terms has both infinitely many negative terms and infinitely many positive terms.

They effectively devised the theory of mass and charge renormalization, in which the infinity in the momentum scale is cut-off by an ultra-large regulator, Λ ( which could ultimately be taken to be infinite — infinities reflect the pileup of contributions from an infinity of degrees of freedom at infinitely high energy scales .).

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.

6 ) at a finite distance from the axis ( or with an infinitely distant object, a point which subtends a finite angle at the system ) is, in general, even then not sharply reproduced, if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop ; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil.

To derive the equations of aerodynamics, fluid properties such as density and velocity are assumed to be well-defined at infinitely small points, and to vary continuously from one point to another.

At that scale the coastline appears as a momentarily shifting, potentially infinitely long thread with a stochastic arrangement of bays and promontories formed from the small objects at hand.

They show how our conscious experience can discriminate between infinitely different possible scenes and details ( differentiation ) because it integrates those details from our sensory systems, while the integrative nature of consciousness in this view easily explains how our experience can seem unified as one whole despite all of these individual parts.

He advises choosing ones company carefully, to avoid being corrupted by immoral people, and while arguing that material wealth is no sin in itself, it is too likely to distract one from the infinitely more important spiritual wealth which is found in Christ.

It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes congruent to 3 ( mod 4 ).

The configuration equivalent to a flat, infinitely conductive plate is achieved by placing an image dipole ( green arrow at left of schematic ) at twice the distance from the planet ’ s dipole to the magnetopause along the planet-Sun line.

Thus the paradox of creating new information, information itself, or creating existence itself and an information system such as a cognitive system into existence from a position of infinitely knowing, becomes a self-refuting argument and defies the listed " omni " attributes.

This again however would defy omniscience, and would again claim the creation of new information, even if imagined, from a position of boundless and limitless omniscience, or a position of already infinitely knowing everything there could ever be known.

However, infinitely large forces repel the particle if it touches the walls of the box, preventing it from escaping.

Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring ...

However, one minister complained that " the mischief arising from the spreading of such a pernicious publication The Age of Reason was infinitely greater than any that could spring from limited suffrage and septennial parliaments " ( other popular reform causes ).

his being infinitely happy in himself from all eternity, and from his goodness manifested in his works, that he could have no other design in creating mankind than their happiness ; and therefore he wills their happiness ; therefore the means of their happiness: therefore that my behaviour, as far as it may be a means of the happiness of mankind, should be such … thus the will of God is the immediate criterion of Virtue, and the happiness of mankind the criterion of the wilt of God ; and therefore the happiness of mankind may be said to be the criterion of virtue, but once removed …( and )… I am to do whatever lies in my power towards promoting the happiness of mankind.

In effect it defined the geoid ( mean sea level ) in terms of a particular level of gravitational time dilation relative to a notional observer located at infinitely high altitude.

With such vast technological improvements, the Vikings began making increasingly more ocean voyages, as their ships were infinitely more sea worthy.

The correct language of heraldry is almost infinitely flexible and virtually any image may be blazoned in a correct manner, for example " sky proper " might be blazoned simply Azure, whilst " waves of the sea " might be blazoned correctly as Azure, 3 bars undee argent which would provide 3 wavy thick white lines on a blue field.

This is due to the surface effect of a real-world solid: a real-world solid is not infinitely extended with electrons and ions repeatedly filling every primitive cell over all Bravais lattice sites.

The incident electron beam diverges and electrons in the beam have a range of energies, so in practice, the Ewald sphere is not infinitely thin as it is theoretically modeled.

The background is the rather stiff and massive background of atomic nuclei and core electrons which we will consider to be infinitely massive and fixed in space.

" I am so infinitely small now that I can see millions of orbiting electrons.

An electron mode depends on the mass of the electrons, but the ions may be assumed to be infinitely massive, i. e. stationary.

In other words, the circuit behaves as if the electrons were flowing infinitely fast.

Since this number is large, at least 1836, it is commonly taken to be infinite in theoretical analyses, that is, either the electrons are assumed to be massless or the ions are assumed to be infinitely massive.

Some sets are infinite ; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by, has infinitely many elements, and we cannot use any normal number to give its size.

It follows that there are also infinitely many solutions if c is a multiple of the greatest common divisor of a and b. If c is not a multiple of the greatest common divisor of a and b, then the Diophantine equation ax + by = c has no solutions.

The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.

Being an individual man is a thing that has been abolished, and every speculative philosopher confuses himself with humanity at large ; whereby he becomes something infinitely great, and at the same time nothing at all.

* This data type has the advantage over arrays that it is infinitely expandable.

If has finite norm, then is infinitely close to.

Since is a compact operator, is infinitely close to and therefore one has also.

God has infinitely many other attributes which are not present in our world.

* An apeirogon is an infinite sequence of sides and angles, which is not closed but it has no ends because it extends infinitely.

The barriers outside a one-dimensional box have infinitely large potential, while the interior of the box has a constant, zero potential.

This also has the effect of turning a position eigenstate ( which can be thought of as an infinitely sharp wave packet ) into a broadened wave packet that no longer represents a ( definite, certain ) position eigenstate.

when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarising herself with theory's knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius.

That is, the electromagnetic field has infinitely more degrees of freedom, corresponding to the different directions in which the photon can be emitted.

A Koch curve has an infinitely repeating self-similarity when it is magnified.

The general government, by uniting and calling into action the pecuniary resources of the states, has created a new capital stock of several millions of dollars, which, with that before existing, is directed into every branch of business, giving life and vigor to industry in its infinitely diversified operation.

Because the hotel has infinitely many rooms, we can move the guest occupying room 1 to room 2, the guest occupying room 2 to room 3 and so on, and fit the newcomer into room 1.

The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years.

Newsweek said that the film " has no more sense of its own ludicrousness than a village idiot stumbling in manure ", but a later article read: " Astoundingly photogenic, infinitely curvaceous, Sharon Tate is one of the most smashing young things to hit Hollywood in a long time.

Since the real numbers can be used to represent points along an infinitely long line, this implies that a line segment of length 1, which is a part of that line, has the same number of points as the whole line.

Geometrically this means that every contour ellipsoid is infinitely thin and has zero volume in n-dimensional space, as at least one of the principal axes has length of zero.

A circle has infinitely many axes of symmetry, for the same reason.

For example, it is known that the Fatou set of a rational map has either 0, 1, 2 or infinitely many components.

* The straightedge is infinitely long, but it has no markings on it and has only one edge, unlike ordinary rulers.