Interestingly, the halting paradox still applies to such machines ; although they determine whether particular Turing machines will halt on particular inputs, they cannot determine, in general, if machines equivalent to themselves will halt.

The name " quine " was coined by Douglas Hofstadter, in his popular science book Gödel, Escher, Bach: An Eternal Golden Braid, in the honor of philosopher Willard Van Orman Quine ( 1908 – 2000 ), who made an extensive study of indirect self-reference, and in particular for the following paradox-producing expression, known as Quine's paradox:

An often-cited theory published by R. A. Fisher in 1930 that attempts to resolve the paradox posits that such traits are the results of explosive positive feedback loops that have as their starting points particular sexual preferences for features that confer a survival advantage and thus " become established in the species.

Thus, the so-called blub paradox ( after a hypothetical programming language of average complexity called ' Blub ') says that anyone preferentially using some particular programming language will ' know ' that it is more powerful than some, but not that it is less powerful than others.

Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox.

But, if the question is inherently required by the concept of omnipotence, then it seems the logic which allows it to be inherently required is a paradox since the particular concept of omnipotence which requires it is a paradox.

In a 1902 letter, he announced the discovery to Gottlob Frege of the paradox in Frege's 1879 Begriffsschrift and framed the problem in terms of both logic and set theory, and in particular in terms of Frege's definition of function ; in the following, p. 17 refers to a page in the original Begriffsschrift, and page 23 refers to the same page in van Heijenoort 1967:

Arrow stiffness ( spine ) is an important parameter in finding arrows that will shoot accurately from any particular bow ( see Archer's paradox ), the spine varying with both the construction and length of the arrow.

He was also a gifted logician with theories on the insolubles and in particular the liar paradox.

Curry's paradox uses a particular kind of self-referential conditional sentence, as demonstrated in this example:

It is closely analogous to several other well-known paradoxes, in particular the Barber paradox and Russell's paradox.

In the same manner, for Heraclitus's paradox, a river has the same formal cause, although the material cause ( the particular water in it ) changes with time, and likewise for the person who steps in the river.

Much commentary has been made on this particular paradox ; many assert that it finds a loophole in common sense.

It is a particular example of the reversibility paradox.

In particular, on d ' Alembert's paradox, he considers another possible route to the creation of drag: instability of the potential flow solutions to the Euler equations.

However, this resolution is invalid, since the paradox is proved by contradiction: assuming that there is any uninteresting number, we arrive to the fact that that same number is interesting, hence no number can be uninteresting ; its aim is not in particular to identify the interesting or uninteresting numbers, but to speculate whether any number can in fact exhibit such properties.

As the paradox lies in the definition of " interesting ", it applies only to persons with particular opinions on numbers: if one's view is that all numbers are boring, and one finds uninteresting the observation that 0 is the smallest boring number, there is no paradox.

To resolve this paradox, Hegel adopts a method whereby the knowing that is characteristic of a particular stage of consciousness is evaluated using the criterion presupposed by consciousness itself.

In particular, he claimed that such an approach resolved the liar paradox.

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.

A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the set of real numbers and the set of natural numbers do not have the same cardinal number.

* In situ hybridization shows which cells are expressing a particular RNA transcript.

Besides the advantages offered by such a plan, in setting immediately before the eyes of the student the final results of the investigation in a more concrete form, and thereby rendering easier his insight into the nature of particular Indo-European languages, there is, I think, another of no less importance gained by it, namely that it shows the baselessness of the assumption that the non-Indian Indo-European languages were derived from Old-Indian ( Sanskrit ).

Relationship-An establishing shot might be a long shot of a room that shows all the characters from a particular scene.

However, even though it cannot be determined whether a particular file is incompressible, a simple theorem about incompressible strings shows that over 99 % of files of any given length cannot be compressed by more than one byte ( including the size of the decompressor ).

The work shows that the transcription start site for genes expressed in a particular tissue, are nucleosome depleted while, the same set of genes in other tissue where they are not expressed, are nucleosome bound.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

There is speculation that Regiomontanus had arrived at a theory of heliocentrism before he died ; a manuscript shows particular attention to the heliocentric theory of the Pythagorean Aristarchus, mention was also given to the motion of the earth in a letter to a friend.

* Though normal television programming resumed after nearly a full week of news coverage following the attack, some daily talk shows such as The Tonight Show with Jay Leno, Late Night with Conan O ' Brien, The Daily Show and Late Show with David Letterman took additional time before beginning to broadcast new installments, with Letterman in particular stating that he was not sure he wanted to continue to do the show.

The hypothesis that the Ancient Roman custom of crucifixion may have developed out of a primitive custom of arbori suspendere — hanging on an arbor infelix ( unfortunate tree ) dedicated to the gods of the nether world — is rejected by William A. Oldfather, who shows that this form of execution ( the supplicium more maiorum, punishment in accordance with the custom of our ancestors ) consisted of suspending someone from a tree, not dedicated to any particular gods, and flogging him to death.

In particular, Viola's obsession with capturing the essence of emotion through recording of its extreme display began at least as early as his 1976 work, The Space Between the Teeth, a video of himself screaming, and continues to this day with such works as the 45-second Silent Mountain ( 2001 ), which shows two actors in states of anguish.

In addition, critics of Ethnic American reality shows frequently state that the portrayals of a particular ethnic group are inaccurate or fictionalized as opposed to " real ".

The matrix M may be regarded as a diagonal matrix D that has been re-expressed in coordinates of the basis P. In particular, the one-to-one change of variable y = Pz shows that z < sup >*</ sup > Mz is real and positive for any complex vector z if and only if y < sup >*</ sup > Dy is real and positive for any y '; in other words, if D is positive definite.

Analysis of a particular antenna ( such as a Hertzian dipole ), shows that this constant is, where is the free-space wavelength.

* Iron Maidens famous fictional mascot, Eddie, was lobotomised on-stage during one of Maiden's live shows ; this concert was filmed for German TV but that particular segment was cut out due to being deemed " Too violent ".

British shows are also sometimes shown on the three commercial television networks in Australia ; in particular Network Seven screened many popular UK sitcoms during the 1970s.

But the typicality theorem shows that, absent some particular reason to believe one of those special initial conditions was in fact realized, Born rule behavior is what one should expect.

The latter shows that the coefficient of X < sup >− 1 </ sup > in ƒ is of particular interest ; it is called formal residue of ƒ and denoted Res ( ƒ ).

A more detailed study by the Brazilian Center for Physics Research ( CBPF ) on the element's isotopes shows similar results ( in particular that < sup > 296 </ sup > Uus is the most stable isotope in its region ), but goes further up to < sup > 337 </ sup > Uus.

Moreover, Gödel's second incompleteness theorem shows that the consistency of sufficiently strong effective theories of arithmetic can be tested in a particular way.

Apollo comes in for particular ridicule as Ovid shows how irrational love can confound the god out of reason.

Another artifact from the 1st dynasty shows a cow lying down on an ivory engraving with the inscription " Hathor in the Marshes " indicating her association with vegetation and the papyrus marsh in particular.

In this overture he shows how folk songs could be given symphonic dimensions while paying particular attention to the element of protyazhnaya or melismatically elaborated lyric song.