Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the " no cloning theorem ", which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results.

* Similarly, cloning would violate the no teleportation theorem, which says classical teleportation ( not to be confused with entanglement-assisted teleportation ) is impossible.

Teleportation does not result in the copying of qubits, and hence is consistent with the no cloning theorem.

In standard quantum mechanics, it is generally accepted that the no cloning theorem prevents superluminal communication via quantum entanglement alone, leading to the no-communication theorem.

This is known as quantum indeterminacy, and underlies results such as the Heisenberg uncertainty principle, information-disturbance theorem and no cloning theorem.

The party's policies include a " Progressive Expenditure Tax " ( with no tax payable on any income that is saved or invested ), universal living allowance tied to basic per capita living costs, rejection of the Goods and Services Tax ( GST ) and other taxes for general revenue that it views as regressive, federal funding for the education of students attending non-government schools to be based on an equitable distribution and increased diversification in overseas trade to broaden the base for growth, and on opposition to abortion, euthanasia, therapeutic cloning and same-sex marriage.

The Asgard are no longer capable of traditional reproduction and instead perpetuate themselves through cloning, as they have the technology to upload and store Asgard consciousnesses and transfer them to new bodies.

The cat showed no negative side effects from the cloning and is alive and healthy.

They also claim that cloning is no more inhumane than breeding.

Since 2001, political efforts have been mounting in many countries to ban human cloning, impelled by a sense of its abhorrence and imminence, while rumors abound that the first human clones may already have been produced, the most famous example being a claim by the extraterrestrial worshiping Raelians, a religious group who have offered no proof to support their extraordinary claims.

The Asgard are no longer capable of traditional reproduction and instead perpetuate themselves through cloning, as they have the technology to upload and store Asgard consciousnesses and transfer them to new bodies.

The Hate-Monger was an ordinary man with no superhuman powers, created as the result of cloning and genetic engineering.

The Kennel Club criticised the entire concept of dog cloning, on the grounds that their mission is to " To promote in every way the general improvement of dogs " and no improvement can occur if replicas are being created.

The race is a step up from cloning in that no two In Vitroes are alike ; however they can share DNA with another In Vitro created from the same batch of constructed chromosomes, which would make two such individuals siblings.

The fact that cloning was illegal at the time of his father's murder causes the Central Computer to declare that no crime was committed, as the only legal remedy in place at the time was for one clone or the other to be destroyed.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

has no zero in F. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed.

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

* Metamath-a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems ; while the Metamath language is not accompanied with an automated theorem prover, it can be regarded as important because the formal language behind it allows development of such a software ; as of March, 2012, there is no " widely " known such software, so it is not a subject of " automated theorem proving " ( it can become such a subject ), but it is a proof assistant.

This incompleteness result is similar to Gödel's incompleteness theorem in that it shows that no consistent formal theory for arithmetic can be complete.

The Sylow 2-subgroups are either cyclic, which is easy to handle using the transfer map, or generalized quaternion, which are handled with the Brauer – Suzuki theorem: in particular there are no simple groups of 2-rank 1.

The three classes are groups of GF ( 2 ) type ( classified mainly by Timmesfeld ), groups of " standard type " for some odd prime ( classified by the Gilman – Griess theorem and work by several others ), and groups of uniqueness type, where a result of Aschbacher implies that there are no simple groups.

The Gauss-Markov theorem shows that the OLS estimator is the best ( minimum variance ), unbiased estimator assuming the model is linear, the expected value of the error term is zero, errors are homoskedastic and not autocorrelated, and there is no perfect multicollinearity.

In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

This contradiction means there are no counterexamples at all and that the theorem is therefore true.

The intuitive statement of the four color theorem, i. e. ' that given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color ', needs to be interpreted appropriately to be correct.

In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, " every planar graph is four-colorable " (; ).

His concept " Dyson's transform " led to one of the most important lemmas of Olivier Ramaré's theorem that every even integer can be written as a sum of no more than six primes.

The theorem is stating two things: first, that 1200 can be represented as a product of primes, and second, no matter how this is done, there will always be four 2s, one 3, two 5s, and no other primes in the product.

Gödel's completeness theorem says that a deductive system of first-order predicate calculus is " complete " in the sense that no additional inference rules are required to prove all the logically valid formulas.

It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

# Reducing the theorem to sentences ( formulas with no free variables ) in prenex form, i. e. with all quantifiers ( and ) at the beginning.

Next we consider a generic formula φ ( which no longer uses function or constant symbols ) and apply the prenex form theorem to find a formula ψ in normal form such that φ ≡ ψ ( ψ being in normal form means that all the quantifiers in ψ, if there are any, are found at the very beginning of ψ ).

As shown by the Lemma above, we only need to prove our theorem for formulas φ in R of degree 1. φ cannot be of degree 0, since formulas in R have no free variables and don't use constant symbols.

To perpetuate wealth control led by small groups of individuals who played no role in its creation prevents those with real initiative from coming to the fore, and is basically anti-democratic.

Winter annuals are important ecologically, as they provide vegetative cover that prevents soil erosion during winter and early spring when no other cover exists and they provide fresh vegetation for animals and birds that feed on them.

This is often called the " no hiding " rule, since it prevents players from placing their first shots where their opponent must traverse completely though the guarded centre ring to hit them and avoid fouling.

Meconium ileus should be distinguished from meconium plug syndrome, in which a tenacious mass of mucus prevents the meconium from passing and there is no risk of intestinal perforation.

It is a de-facto non-partisan democracy since no law prevents the formation of political parties.

David prevents his associates from killing Saul, because doing so would prove the former no more worthy than the latter ; Instead, David merely steals Saul's spear and water jug.

For example, if X goes to a restaurant and, by mistake, takes Y's scarf instead of her own, she has physically deprived Y of the use of the property ( which is the actus reus ) but the mistake prevents X from forming the mens rea ( i. e., because she believes that she is the owner, she is not dishonest and does not intend to deprive the " owner " of it ) so no crime has been committed at this point.

" Hestia's omission from some lists of the Twelve Olympians is sometimes taken as illustration of her passive, non-confrontational nature – by giving her Olympian seat to Dionysus she prevents heavenly conflict – but no ancient source or myth describes such a surrender or removal.

The journalist noted that ' according to legal advice taken by The Sunday Age there is no provision that prevents the naming of an ASIS agent '.

These messages are used to periodically report on the status of PVCs, which prevents data from being sent into black holes ( that is, over PVCs that no longer exist ).

Significantly, despite popular belief to the contrary, a system's being " fail-safe " means not that failure is impossible / improbable, but rather that the system's design prevents or mitigates unsafe consequences of the system's failure ; that is, if and when a " fail-safe " system " fails ", it is " safe " or at least no less safe than when it is operating correctly.

Note that there is no restriction ( except possibly consideration of the neighbors ) that prevents using more than one house code within a single house.

Thus, from the starting position, it takes little skill and no imagination to avoid losing, and nothing in the rules prevents games from being interminable.

The no auto-summary command prevents automatic route summarization on classful boundaries, which would otherwise result in routing loops in discontiguous networks.

:" The Conservative belief that there is some law of nature which prevents men from being employed, that it is ' rash ' to employ men, and that it is financially ' sound ' to maintain a tenth of the population in idleness for an indefinite period, is crazily improbable-the sort of thing which no man could believe who had not had his head fuddled with nonsense for years and years.

There is little or no data to support the concept that activity adjustment prevents carpal tunnel syndrome.

The section of Highway 1 that crosses the Malahat northwest of Victoria has no stoplights yet, but is tightly pinched by rugged terrain that prevents widening to four lanes and sometimes forces closure for hours at a time after a traffic accident.

The suit prevents electrical current from flowing through the body, and has no theoretical voltage limit.

The Wild and Free-Roaming Horses and Burros Act of 1971 prevents the capture of mustangs from the wild for commercial use, and though the law has been weakened in recent years, " wild " mustangs and other completely untamed horses are still no longer used on the rodeo circuit, as bigger, more powerful animals that are sufficiently domesticated to be handled from the ground for veterinary care, travel, and stabling in small pens are more desirable as rodeo stock.

This automatic vote prevents the Code from remaining in effect if students no longer support it.

However, due to Hubble's law regions sufficiently distant from us are expanding away from us much faster than the speed of light ( special relativity prevents nearby objects in the same local region from moving faster than the speed of light with respect to each other, but there is no such constraint for distant objects when the space between them is expanding ; see uses of the proper distance for a discussion ), and the expansion rate appears to be accelerating due to dark energy.

During a two-year period, the assembly can meet on its own for no more than 91 days, and this often prevents them from passing all the legislation they intend to.

He endeavours to get through, and succeeds in doing so, after much struggling as far as his shoulders ; but finding that the soot is compressed hard all around him, by his exertions, that he can recede no farther ; he then endeavours to move forward, but his attempts in this respect are quite abortive ; for the covering of the horizontal part of the Flue being stone, the sharp angle of which bears hard on his shoulders, and the back part of his head prevents him from moving in the least either one way or the other.