As the practical engineer might say, the proof of the pudding is in the eating.

The proof is in the pudding!

The proof is in the pudding.

I must confess that I prefer the Liberal who is personally affected, who is willing to send his own children to a mixed school as proof of his faith.

In any event, the critical productivity of that time is abundant proof that if he was taking laudanum, it was never in command of him to the extent that it had been during his vagrant years.

The appointment of U Thant of Burma as the U.N.'s Acting Secretary General -- at this writing, the choice appears to be certain -- offers further proof that in politics it is more important to have no influential enemies than to have influential friends.

The first is the strictly scientific, which demands concrete proof and therefore may err on the conservative side by waiting for evidence in the flesh.

The idea of the proof is this.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

so that the absence of the hymen is by no means positive proof that a girl has had sex relations.

Most of them, the world over, operate on the same principle by which justice is administered in France and some other Latin countries: the customer is to be considered guilty of abysmal ignorance until proven otherwise, with the burden of proof on the customer himself.

Schwab also declared there is no proof of Weinstein's entering a conspiracy to use the U.S. mails to defraud, to which federal prosecutor A. Lawrence Burbank replied:

level ( when the standard of proof is high, the chances of overlooking

Chaitin prefaces his definition with: " I'll show you can't prove that a program is ' elegant '"— such a proof would solve the Halting problem ( ibid ).

Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers ' common measure is in fact the greatest.

Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.

When one attempts to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof.

It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

There is some documentary proof that the Romans named the hot sulfur springs of Aachen Aquis-Granum, and indeed to this day the city is known in Italian as Aquisgrana, in Spanish as Aquisgrán and in Polish as Akwizgran.

The dreamer reported that he didn't realize he was in the dream world but the man whom he met in his dream remind him about this and point out that his experience is a proof of life after death.

Although he didn't realise it at the time, he had discovered proof of the " spokes " of Saturn, dark shadows running parallel to the circular paths of the rings.

As an adult, Fester defended his father's strictness, pointing to his own character as proof of its effectiveness: " I didn't become what I am by accident!

He mentioned to the audience that he didn't expect anyone in the hall to live long enough to see a proof of this final result.

The space C is infinite dimensional, and the general proof for the infinite dimensional case requires the axiom of choice or something equivalent, which didn't exist in 1912, so how did Helly prove it?

She didn't have any proof of this so she had to look for it.

* ( Purely analytic proof of the theorem that between any two values which give results of opposite sign, there lies at least one real root of the equation ).

To give a proof of a " yes " instance, one must specify a non-empty subset which does sum to zero.

" To give a proof of a " no " instance one must specify a non-empty subset which does sum to zero, which is easily verified.

" He added that the public as well as proper organizations were entitled to such proof and that he was ready and willing to give such proof in detail.

The theorem that bears his name may not have been his discovery, but he was probably one of the first to give a deductive proof of it.

Hilbert produced an innovative proof by contradiction using mathematical induction ; his method does not give an algorithm to produce the finitely many basis polynomials for a given ideal: it only shows that they must exist.

Such reactors often give off radioactive waste that is especially hard to safely dispose, since it must be stored in radioactive proof locations, such as underground.

Together, these first two examples give a different proof that n-dimensional Euclidean space is separable.

These papers are together believed to give a complete proof, and there are several ongoing projects to shorten and simplify this proof.

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

Therein he attacked some often-used surrealist techniques by proclaiming, " Surrealism will at least have served to give experimental proof that total sterility and attempts at automatizations have gone too far and have led to a totalitarian system.

If, however, the subject lives a life of great extravagance, tell him he, too, can afford to give largely, the proof of his opulence being evident in his expenditure.

They must give us proof, strong as holy writ, that they have washed their hands and are worthy again to be trusted.

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

We will now give the precise meaning of this statement as well as its proof.

The MPAA's R rating is definitive proof that the organization either will never give the NC-17 rating for violence alone, or was intimidated by the subject matter.

The course of studies lasted ten years, during which time their burses continued ; but if, at the end of ten years, they had not given proof of their ability, either as teachers or as preachers, they had to give up their burse.

In fact, it is possible to give a proof that is a Noetherian ring without appealing to its order structure and this proof applies more generally to principal ideal rings ( i. e., rings in which every ideal is generated by a single element ).

Thereafter, to protect themselves, they style themselves " white men from the stars " – sorcerer-gods – and are required to give regular proof of their divinity, considerably straining both their nerves and their ingenuity.

" Concerning the author, the critic said, " If ever on earth there lived a man who kept the law of Christ, and could give proof of it, and be absolutely unconscious that he was giving it to them, it is this man whom the Mongols called ' our Gilmour.

She claimed to have proof that " 69 of the injured were given no medical care " and that " 80 percent of the surviving hostages are potential future invalids, including future ( occurrence of ) cancers, ( and there is a possibility that ) women who were subjected to the gas attack ( could ) give birth to defective babies ".