Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

Practical applications are made impossible due to the no-cloning theorem, and the fact that quantum field theories preserve causality, so that quantum correlations cannot be used to transfer information.

In fact, the neo-Piagetian theories of cognitive development have fully integrated the developmental conception of changes in thought with age with cognitive models of information processing.

These theories were given credence by the fact that when Germany surrendered in November 1918, its armies were still in French and Belgian territory, Berlin remained 450 miles from the nearest front, and the German armies retired from the field of battle in good order.

Although current trends in genetics have raised questions amongst critical academics concerning parallels between pre-war attitudes about eugenics and current " utilitarian " and social theories allegedly related to Darwinism, they are, in fact, only superficially related and somewhat contradictory to one another.

Many physicists believe that the above phenomena are in fact impossible, and that future theories of gravity will prohibit them.

It is commonly believed that this matching is unlikely to be a coincidence, and is often quoted as one of the main motivations to further investigate supersymmetric theories despite the fact that no supersymmetric partner particles have been experimentally observed ( March 2011 ).

Subsequent research by the likes of Hutton and Heselton has shown that in fact the New Forest coven was probably only formed in the early 20th century, based upon such sources as folk magic and the theories of Margaret Murray.

Ultimately, the genetics have in fact not yet told us anything new ; all these theories were well in place amongst archaeologists long before attempts were made to identify historical population movements with genetics.

Such conspiracy theories rely on the fact that his body was never found.

In fact, the Michelson-Gale-Pearson experiment in 1925 was proposed specifically as a test to confirm the relativity theory, although it was also recognized that such tests, which merely measure absolute rotation, are also consistent with non-relativistic theories.

There are relations between these two theories as well, and these relations are in fact strong enough to allow them to be identified.

The fact that most of the early post-translational modifications found were concentrated within the tail extensions that protrude from the nucleosome core lead to two main theories regarding the mechanism of histone modification.

Methodist theories propose an answer to question set two and proceed to use this to establish what we, in fact, know.

At around the same time, the atomic theory and the corpuscular theory of light ( as updated by Einstein ) first came to be widely accepted as scientific fact ; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively.

The common form of the razor, used to distinguish between equally explanatory hypotheses, may be supported by the practical fact that simpler theories are easier to understand.

However, the fact that empirical evidence does not serve to determine between alternative theories does not necessarily imply that all theories are of equal value, as scientists often use guiding principles such as Occam's Razor.

While dark matter is estimated to comprise 83 % of the mass of matter in the universe, most of its properties remain a mystery due to the fact that it neither absorbs nor emits electromagnetic radiation, and there are many competing theories regarding what dark matter is actually made of.

Eventually, in the face of Van Leeuwenhoek's insistence, the Royal Society arranged to send an English vicar, as well as a team of respected jurists and doctors, to Delft, to determine whether it was in fact Van Leeuwenhoek's ability to observe and reason clearly, or perhaps the Royal Society's theories of life itself that might require reform.

Moreover, as the energy scale increases, the strength of the electromagnetic interaction approaches that of the other two fundamental interactions, a fact important for grand unification theories.

Even though the theories of Thomas Malthus would predict that famines reduce the size of the population commensurate with available food resources, in fact even the most severe famines have rarely dented population growth for more than a few years.

Unlike his father, Tom Jr. is not just a tinkerer ; he relies on scientific and mathematical theories, and, according to critic Robert Von der Osten, " science the books is, in fact, understood to be a set of theories that are developed based on experimentation and scientific discussion.

In fact, because of atmospheric refraction and because the sun appears as a disk and not a point, part of the midnight sun may be seen on the night of the northern summer solstice up to about 50 ′ () south of the Arctic Circle ; similarly, on the day of the northern winter solstice, part of the sun may be seen up to about 50 ′ north of the Arctic Circle.

In fact, f coincides with its Taylor series at a in any disk centered at that point and lying within the domain of the function.

However, a report released in January 2005 found that the drives were in fact an artifact of an inconsistent inventory system: the report concludes that 12 barcodes were issued to a group of disk drives that needed only 10, but the two surplus barcodes nevertheless appeared on a master list.

In fact, Windows assigns the next free drive letter to the next drive it encounters while enumerating the disk drives on the system during installation.

It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function.

In fact signals read by a disk read-and-write head are converted by a disk controller, then transmitted over the peripheral bus, then converted again by the host adapter into the suitable format for the motherboard's bus, and then read by the CPU.

The newer toolsets increased the performance of the machine by up to 10 %, due to the fact that less had to be loaded from disk and their highly optimized routines compared to the older toolsets ( pre-GS / OS based ).

This is, in fact, a cross-cap glued to a disk.

Today, an end-user, in most cases, should never perform a low-level formatting of an IDE or ATA hard drive, and in fact it is often not possible to do so on modern hard drives because the formatting is done on a servowriter before the disk is assembled into a drive in the factory.

Even with the improvements, the first 4 clusters of the MFT remain unmovable by the Windows defragmentation API, resulting in the fact that some defragmenters will store the MFT in two fragments: The first 4 clusters wherever they were placed when the disk was formatted, and then the rest of the MFT at the beginning of the disk ( or wherever the defragmenter's strategy deems to be the best place ).

This effort was helped by the fact that the Amiga version of X * Press X * Change was distributed on a floppy disk that had, by mistake, some random portions of the software source code on some of its unused blocks.

Since it was now technically possible to store a single fact in a single place and access that using random access disk, those suggesting that " Data Management " was more important than " Process Management " used arguments such as " a customer's home address is stored in 75 ( or some other large number ) places in our computer systems.

DiskDoctor in fact changed autostart disks bootblocks into standard AmigaDOS-based ones, renaming a disk with " Lazarus " namedisk, and made the autostart disk unusable.

It is distinguished technically by the fact that the ray flowers, when present, are sterile, and by the presence on the disk flowers of a pappus that is of two awn-like scales that are cauducous ( that is, easily detached and falling at maturity ).

Indeed, in using the Toolbox to help boot the machine, a rudimentary Macintosh environment was initialized long before loading the System suitcase from disk ( in fact before ROMs on NuBus cards were executed ), which is when the decision to use 24-bit or 32-bit addressing has to be made ( hence why the System 7's support for 32-bit addressing requires 32-bit clean ROMs, as older Mac ROMs did not have support for this ).

Because the magnetic surface is right next to the writing surface ( rather than somewhere outside the disk itself ) the magnetic writing can be done at a much higher resolution-in fact, the resolution of the laser spot doing the heating up.

In fact, the star formation rate of the outer disk is approximately two times greater than the inner disk because it is more efficient per unit of stellar mass.

In fact: The Amiga version could not be copied onto the hardrive due to copy protection and its custom disk format.

The realization that we live in a galaxy, and that there were, in fact, many other galaxies, parallels discoveries that were made about the Milky Way and other nebulae in the night sky.

In fact, it has been theorized that a quasar could form as the Andromeda Galaxy collides with our own Milky Way galaxy in approximately 3 – 5 billion years.

The obscure mechanism of cosmic ray production at galactic distances is partly a result of the fact that ( unlike other radiations ) magnetic fields in our galaxy and other galaxies bend cosmic ray direction severely, so that they arrive nearly randomly from all directions, hiding any clue of the direction of their initial sources.

This religion, unlike so many others in the galaxy, is unique in that the religious figures are in fact physical ( but non-corporeal ) entities, although not on the same plane of existence ; see Bajoran Prophets.

It has been proposed by astrophysicists D. S. Mathewson, V. L. Ford and N. Visvanathan that the SMC may in fact be split in two, with a smaller section of this galaxy behind the main part of the SMC ( as seen from our perspective ), and separated by about 30, 000 ly.

It has been proposed by astrophysicists D. S. Mathewson, V. L. Ford and N. Visvanathan that the SMC may in fact be split in two, with a smaller section of this galaxy behind the main part of the SMC ( as seen from our perspective ), and separated by about 30, 000 ly.

The survey also confirmed earlier theories that the Milky Way galaxy was in fact being pulled towards a much more massive cluster of galaxies near the Shapley Supercluster which lies beyond the Great Attractor.

( In fact, Walter Baade's failure to find them in the Andromeda galaxy led him to suspect that the galaxy was much farther away than predicted, to reconsider the calibration of Cepheid variables, and to propose the concept of stellar populations.

The location was also said to fit the " other end of the galaxy " location since the galaxy is not in fact a disc, but a spiral — and from the edge, the other end of a spiral lies at the centre.

The fact that the lenticular galaxy distribution rises with increasing observed axial ratio implies that lenticulars are dominated by a central bulge component.

The planet, which is in fact a sentient life form itself, is home to life unlike any other in the galaxy, including organic spaceships.

However Londo was saved by the fact that at the same time in another part of the galaxy, a fleet led by John Sheridan was fighting their final battle against the Shadows and Vorlons at Corianna 6 and the Vorlons called in all their remaining ships to help.

This fact is important if position in the galaxy is related to habitability, as suggested by the Rare Earth hypothesis.

However, the emissary was, in fact, seeking a greater talent for war, as the aliens routinely breed warriors to fight for them across the galaxy.

The Milky Way has more than 20 known dwarf galaxies orbiting it, and recent observations have also led astronomers to believe the largest globular cluster in the Milky Way, Omega Centauri, is in fact the core of a dwarf galaxy with a black hole in its center, which was at some time absorbed by the Milky Way.

However, it is possible that the galaxy is oriented in such a way that it appears spherical to an observer on Earth but is in fact elliptical.

NGC 3109 is classified as a Magellanic type irregular galaxy, but it may in fact be a small spiral galaxy.

If the Pinwheel Galaxy were in fact a distinct galaxy and could be observed to be rotating on a timescale of years, its orbital velocity would be enormous and there would clearly be a violation of the universal speed limit, the speed of light.

Also, it is now known that the nova Shapley referred to in his arguments was in fact a supernova, which do indeed temporarily outshine the combined output of an entire galaxy.

In Magical Project S ( Pretty Sammy TV ), Tsunami is much the same as her series counterpart, except now with a great love for flowers ; in fact, one of her goals as queen of Juraihelm was to " plant flowers across the entire galaxy ".

The central premise concerns the fact that in the original Star Trek, humans were portrayed as the dominant race throughout the galaxy.