* Gödel's Proof ( 2002 revised edition ) by Ernest Nagel and James R. Newman, edited by Hofstadter ( ISBN 0-8147-5816-9 ).

Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.

Post's solution to the problem is described in the demonstration An Example of a Successful Absolute Proof of Consistency offered by Ernest Nagel and James R. Newman in their 1958 Gödel's Proof.

* Ernest Nagel and James R. Newman 1958 Gödel's Proof, New York University Press, Card Catalog Number: 58-5610.

* Nagel, Ernest and Newman, James R., Godel's Proof, New York University Press, 1958.

Their first single, " Down in Mexico ," was an R & B hit in 1956 and appears ( in a re-recording from 1970 — still with Gardner singing the lead ) on the soundtrack of Quentin Tarantino's Death Proof.

* Gödel's Proof by Ernest Nagel and James R. Newman ( 1959 ).

( Proof: If m < n, then we can view R < sup > m </ sup > as a subspace of R < sup > n </ sup >, and the non-empty open subsets of R < sup > m </ sup > are not open when considered as subsets of R < sup > n </ sup >.

Proof: Using the same sum for R ( p, n ) as in Lemma 2, we see that since p < sup > 2 </ sup > > 2n, in fact only the first term is nonzero ; this term is exactly the right-hand side of the above equation.

* Gödel ’ s Proof ( with J. R. Newman, 1958 )

The Hot Wax label, distributed by Buddah Records, was in full operation for about four years, racking up a series of successful records, such as Honey Cone's " Want Ads " ( a number 1 hit on both the Billboard Hot 100 and Billboard R & B Singles charts ), " Stick Up ", and " One Monkey Don't Stop No Show "; " Somebody's Been Sleeping in My Bed " by 100 Proof ( Aged in Soul ); " Westbound Number 9 " by Flaming Ember ; and " Rip Off " by Laura Lee.

Proof: Let S, T be primitive polynomials in R, and assume that their product ST is not primitive, so that some noninvertible element d of R divides all coefficients of ST.

* R. Schoen and S .- T. Yau, " Proof of the positive mass theorem.

* R. Schoen and S. T. Yau, " Proof that the Bondi mass is positive ", Phys.

Proof: By symmetry, it suffices to prove that there is some constant c such that for all bitstrings s

Generally this is in a very small detail, such as the number of leaves on the ear of corn on the recent US Wisconsin state quarter: File: 2004 WI Proof. png.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

* Demonstratio evangelica ( Proof of the Gospel ) is closely connected to the Praeparatio and comprised originally twenty books of which ten have been completely preserved as well as a fragment of the fifteenth.

He famously put the point into dramatic relief with his 1939 essay " Proof of an External World ", in which he gave a common sense argument against scepticism by raising his right hand and saying " Here is one hand ," and then raising his left and saying " And here is another ," then concluding that there are at least two external objects in the world, and therefore that he knows ( by this argument ) that an external world exists.

Proof of second property: since a * b and b * b < sup >− 1 </ sup > are defined, so is a * b * b < sup >− 1 </ sup >=

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

#* Proof: suppose that p is composite, hence can be written with a and Then is prime, but and contradicting statement 1.

#* Proof:, so is a square root of 2 modulo.

* In Hal Clement's short story Proof ( 1942 ), neutronium is the only form of solid matter known to Solarians, the inhabitants of the Sun's interior.

Proof: If there is no possible move, then the lemma is vacuously true ( and the first player loses the normal play game by definition ).

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

( Proof: either 1 is positive or − 1 is positive.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

* Proof of Fermat's Last Theorem is discovered by Andrew Wiles.

Proof: We only give the proof in the simplified case ; the general case is similar.

We say that N is nilpotent if there is some positive integer R such that Af.

for, using the fact that N and N' commute Af and so when R is sufficiently large every term in this expression for Af will be 0.

It is very easy to establish by induction on R that if F is in Af then Af ; ;

It is difficult to measure the direction and magnitude of R directly.

This is not a constant value like Af, but varies with the thickness of the coating and the direction and magnitude of the resultants R and Af of Fig. 6.

If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

But even more important than this is the fact that the direct search by simultaneously varying all operating conditions has produced only one optimal policy, namely, that for the given feed state and R stages.

But Af is vastly larger than R.

These will be numbered in the direction opposite to the flow of the process stream, so that stage R is the T stage from the end.

In the third column is given the optimal policy for stage R, and in the fourth, the resulting state of the stream when this policy is used.

In this case the stage R operating with conditions Af transforms the state of the stream from Af to Af, but only the probability distribution of Af is known.

that is, it is known empirically that names beginning with R are more common than those beginning with Z ; ;

The study of altruism was the initial impetus behind George R. Price's development of the Price equation, which is a mathematical equation used to study genetic evolution.

Kempthorne and his students make an assumption of unit treatment additivity, which is discussed in the books of Kempthorne and David R. Cox.

An alkyl group, generally abbreviated with the symbol R, is a functional group or side-chain that, like an alkane, consists solely of single-bonded carbon and hydrogen atoms, for example a methyl or ethyl group.

Where territory is occupied in the course of hostilities by an enemy's force, even if the annexation of the occupied country is proclaimed by the enemy, there can be no change of allegiance during the progress of hostilities on the part of a citizen of the occupied country ( R v Vermaak ( 1900 ) 21 NLR 204 ( South Africa )).

A natural-born subject owes allegiance wherever they may be, so that where territory is occupied in the course of hostilities by an enemy's force, even if the annexation of the occupied country is proclaimed by the enemy, there can be no change of allegiance during the progress of hostilities on the part of a citizen of the occupied country ( R v Vermaak ( 1900 ) 21 NLR 204 ( South Africa )).

USACC is co-chaired by Tim Cejka, President of Exxon Mobil Corporation and Reza Vaziri, President of R. V.