We shall prove that Af.

We can now prove several lemmas.

We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove " φ is either refutable or satisfiable ".

We seek to prove that there exist two irrational numbers and such that

Say instead we wish to prove proposition p. We can proceed by assuming " not p " ( i. e. that p is false ), and show that it leads to a logical contradiction.

We prove that there exists ( x, y, z ) such that

We should prove that the angular velocity previously defined is independent from the choice of origin, which means that the angular velocity is an intrinsic property of the spinning rigid body.

We will prove these things below ; let us first see an example of this proof in action.

We can prove the cancellation law easily using Euclid's lemma, which generally states that if an integer b divides a product rs ( where r and s are integers ), and b is relatively prime to r, then b must divide s. Indeed, the equation

In 1950, Time quoted Webb: " We don ’ t even try to prove that crime doesn ’ t pay ... sometimes it does " ( Dunning, 210 )

We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.

We shall prove the five lemma by individually proving each of the 2 four lemmas.

We prove that if an increasing sequence is bounded above, then it is convergent and the limit is.

We wish to prove that they are all the same color.

We cannot use Russia's methods, as they only and at best prove that the economy of an agrarian nation can be leveled to the ground ; Russia's thoughts are not our thoughts.

Jim Capaldi used this hiatus to record a solo album, Oh How We Danced, which would prove to be the beginning of a long and successful solo career.

We shall therefore now consider only arguments that prove the theorem directly for any matrix using algebraic manipulations only ; these also have the benefit of working for matrices with entries in any commutative ring.

We prove that this is not true.

We need to prove that some time class TIME ( g ( n )) is strictly larger than some time class TIME ( f ( n )).

We prove that R ( r, s ) exists by finding an explicit bound for it.

We now prove the result for the general case of c colours.

We have given to us a conception A uniting among its constituent marks two that prove to be contradictory, say M and N ; and we can neither deny the unity nor reject one of the contradictory members.

We wish to prove 4T < sup > 2 </ sup >

We do not intend to prove otherwise.

" Under the law of association, transmission of wealth does not apply to the instruments of labour, so cannot become a cause of inequality .... We are socialists ... under universal association, ownership of the land and of the instruments of labour is social ownership ... We want the mines, canals, railways handed over to democratically organised workers ' associations ... We want these associations to be models for agriculture, industry and trade, the pioneering core of that vast federation of companies and societies, joined together in the common bond of the democratic and social Republic.

We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.

We accept and welcome, therefore, as conditions to which we must accommodate ourselves, great inequality of environment ; the concentration of business, industrial and commercial, in the hands of the few ; and the law of competition between these, as being not only beneficial, but essential to the future progress of the race.

We now give an operator theoretic proof for the Cauchy – Schwarz inequality which passes to the C *- algebra setting.

We can then infer that the probability that it has between 600 and 1400 words ( i. e. within k = 2 SDs of the mean ) must be more than 75 %, because there is less than chance to be outside that range, by Chebyshev ’ s inequality.

We may recover the original inequality ( for the case p = 2 ) by using the functions | f | and | g | in place of f and g.

We can write the inequality as:

" We have known for 50 years that the theory of racial inequality can be deadly ... It entails outrages ", Lustiger said.

We note that for any T in B ( H ) the following inequality is satisfied:

We claim that without loss of generality, the latter inequality is always strict ; once we do this the theorem can be proved as follows.

We have the following inequality involving the Pythagorean means

We say about a manifold M that it satisfies a d-dimensional isoperimetric inequality if for any open set D in M with a smooth boundary one has

We take this inequality and switch the role of the operator and the operand, or in other words, we think of S as the operator of convolution with g, and get that S is bounded from to.

His Our Kind: Who We Are, Where We Came From, Where We Are Going ( 1990 ) surveys the broad sweep of human physical and cultural evolution, offering provocative explanations of such subjects as human gender and sexuality and the origins of inequality.

We resume our derivation by expressing the upper bound on our in light of the geometric inequality above:

The album is reminiscent of the artist's earlier, more pop-oriented records and marks a lyrical return to the subject of relationships ( as in the single " Can We Still Be Friends "), as well as his views on social inequality ( as in the songs " Bag Lady " and " Bread ").

We are living at the end of the Cosmic Summer, a time marked by war, disease, and inequality, and we will soon be faced with tragedies on a global scale.