By induction we conclude the statement is true for all r ≥ 0.

By the induction hypothesis,

By the end of the year, Alexander was also distinguished with his induction as a Knight of the Order of the Garter.

By Dr. Zaehner, the author of Mysticism, Sacred and Profane, their deliberate induction is regarded as immoral.

By the 1870s, efficient generators that produced alternating current ( alternators ) were available, and it was found that alternating current could power an induction coil directly, without an interrupter.

By induction, Hilbert's basis theorem establishes that, the ring of all polynomials in n variables with coefficients in, is a Noetherian ring.

By means of mathematical induction, it is easily proven that the above procedure requires the minimal number of moves possible, and that the produced solution is the only one with this minimal number of moves.

By the principle of mathematical induction it follows that the result is true for all natural numbers.

By reasoning using " induction " Bacon meant the ability to gradually generalize a finding based on accumulating data-he advised proceeding by this method ( building a case from the ground up ).

By induction, SO ( n ) therefore has

By Faraday's law of induction we have

By his method of observation and induction as thus explained, his philosophy will be found to be marked off very clearly, on the one hand from the deductive construction of notions of an absolute system, as represented either by Schelling or Hegel, which Cousin regards as based simply on hypothesis and abstraction, illegitimately obtained ; and on the other, from that of Kant, and in a sense, of Sir W. Hamilton, both of which in the view of Cousin are limited to psychology, and merely relative or phenomenal knowledge, and issue in scepticism so far as the great realities of ontology are concerned.

By preventing the clonal expansion of lymphocytes in the induction phase of the immune response, it affects both the cell and the humoral immunity.

By contrast, in an induction motor the rotor rotates at a slower speed than the stator field.

By varying the line frequency with an inverter, induction motors can be kept on the stable part of the torque curve above the peak over a wide range of rotation speeds.

By induction, Axioms ( 3 ) and ( 4 ) are equivalent to the single statement

So, i. e. the commutant of the bicommutant of S is equal to the commutant of S. By induction, we have:

By the early 1990s, when his time of eligibility was beginning to run out, many Puerto Ricans, celebrities and ordinary citizens alike, began to campaign for his induction.

By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction:

The same wire ( in practice a coil of wire ) is moved through the same magnetic field at a known speed v. By Faraday's law of induction, a potential difference U is generated across the ends of the wire, which is equal to BLv.

By induction, the hypothesis implies that M < sup > k </ sup > T

By induction, we assume that for some integer the partially ordered set can be covered by disjoint chains and has at least one antichain of size.

: Proof: By mathematical induction.

By this time word had got around that an American doctor was on the premises.

Suggest the following twenty-first-century amendment: By moving the term `` Republic '' to lower case, substituting the modern phrase, `` move ahead '' for the stodgy `` keep '', and by using the Postmaster's name on every envelope ( in caps, of course, with the `` in spite '' as faded as possible ), the slogan cannot fail.

By odd coincidence, on the evening of her return Shelley chose to read Parisina, which was the latest of the titled poet's successes.

By fixing the tax rate in advance of spending, upper limits are set on expenditures.

By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.

By automobile from New York, for example, you can take a one or two-day tour to Annapolis, Maryland to see the colonial homes and the U.S. Naval Academy ( where you can shoot the dress parade on Wednesdays ) ; ;

By submerging the patient in a tub and rotating the transducer while the scanning goes on, they have been able to get cross-section views of the neck, as shown in Fig. 7, as well as many other hitherto impossible insights.

Reports Jim Lendrum: `` By studying men on the job, we found that two men -- a carpenter and a helper -- can lay a floor faster than three.

By comparing reaction cells sealed from the same manifold temperature dependency corresponding to activation energies ranging from 11 to 18 Af was observed while dependence on the first power of the light intensity seemed to be indicated in most cases.

By Nov. 8, 1958, weakness, specifically involving the pelvic and thigh musculature, was pronounced, and a common complaint was `` difficulty in stepping up on to curbs ''.

By all means the most important distinction is that between those total-cost apportionments which superimpose a distribution of admittedly unallocable cost residues on estimates of incremental or marginal costs, and those other apportionments which recognize no difference between true cost allocation and mere total-cost distribution.

By 800 social and cultural security had been achieved, at least on a simple plane ; ;

By 1871 L. C. Orvis, manager of the `` Western Union Telegraph Company '', expressed willingness to send emergency telegrams on Sundays from his Village drugstore.

By themselves they may not be able to save the life on this planet, but without them there would be very little left worth saving.

By preying on the sick, by playing callously on the hopes of the desperate, by causing the sufferer to delay proper medical care, these medical ghouls create pain and misery by their very activity.

By fall, 443 survivors of this arduous journey were clustered about Fort Snelling, but most of them were sent on to Galena and St. Louis, with a few going as far as Vevay, Indiana, a notable Swiss center in the United States.

By the time her hindquarters were in a standin' position, her knees were on the ground in a prayin' attitude.

By 1926, when the mighty Yanks were at their mightiest, only a few of these were left but they still shone brightest, even beside able and agile rookies like Tony Lazzeri ( who managed never to have one of his epileptic fits on the field ), Mark Koenig, Lou Gehrig, George Pipgras, and gray-thatched Earl Combs.

By a wrenching effort, he managed to hunch and draw in, to take the final fall on his back and shoulders rather than his head.

`` By winning against Bradley, Kentucky and Notre Dame on those teams' home courts, they showed that the home court advantage can be overcome anywhere and that it doesn't take a super team to do it ''.

By mid-June, millions of Americans will take to the road on vacation trips up and down and back and forth across this vast and lovely land.

By July 1, six weeks from now, motel-keepers all over the nation will, by 6 p.m., be switching on that bleak -- to motorists -- sign, `` No Vacancy ''.

By the end of the third act, the artist is dead but the body lingers on, a shell among other shells.

By the time the fielder got his hands on the ball Deegan was rounding third base and heading for home.