What's the difference between infinitesimal and limit?

Infinitesimal


Definition:

  • (a.) Infinitely or indefinitely small; less than any assignable quantity or value; very small.
  • (n.) An infinitely small quantity; that which is less than any assignable quantity.

Example Sentences:

  • (1) The first 2 ms of these transients were described by a linear model in which the fibre is regarded as a rod composed of infinitesimally small, identical segments containing a mass, one undamped elastic element and in the case of relaxed fibres two damped elastic elements in series, or in the case of activated fibres three such elastic elements in series.
  • (2) These equations can be solved easily by stepwise numerical integration involving sucessive infinitesimal rotations (SIR).
  • (3) The present day IBV might be progeny from a unique pool of primordial genome via mutation and host-induced variation, or even persistence of primordial virus as an infinitesimal portion of the population.
  • (4) Examples of current input considered are (1) an infinitesimally brief (Dirac delta function) pulse and (2) a step pulse.
  • (5) Pickup, now 71, recalls the "horrible, infinitesimal detail of how accurate you had to be, partly because you didn't want stones bouncing off the pram into the audience".
  • (6) The chances of Keeler being installed in Downing Street were infinitesimal.
  • (7) For infinitesimal steps the eigen-functions of the diffusion operator are known analytically, while for random motion of arbitrary step size they are determined by diagonalizing the transition matrix appropriate for the step model used.
  • (8) The two principal plasminogen activators (PA) and the two PA-inhibitors are present in infinitesimal concentrations in blood (pM to microM range) and in tissues.
  • (9) Experimental spectra are compared with computer simulations of spectra carried out for isotropic Brownian (limit of infinitesimal step size) and free diffusion (arbitrary step size) models.
  • (10) The infinitesimal change in entropy of a system (dS) is calculated by measuring how much heat has entered a closed system (δQ) divided by the common temperature (T) at the point where the heat transfer took place.
  • (11) However, incidence data indicate the chance of disclosing tumors, non-inflammatory cysts or other serious bone disease in the asymptomatic patient by screening jaw films is infinitesimal.
  • (12) Statistical analysis permitted empirical evaluation of creep of the cellular membrane within the range of infinitesimal stress.
  • (13) "The chances of each of us coming into existence are infinitesimally small," he argues, "and even though we shall all die some day, we should count ourselves fantastically lucky to get our decades in the sun."
  • (14) Of course, fear of risk is actually the bestselling tool of all: it is the basis of the entire insurance industry, whose profit base is predicated on the fact that fear is a very real emotion selling the product, but the statistical probability of anything actually happening, well, that is infinitesimal.
  • (15) The armed seizure of the Crimean parliament, the cynical insistence that Russian troops were not operating in Crimea when they clearly were, and the breakneck speed and flagrant violations involved in organising the Crimean referendum at short notice have been hidden behind a thread of plausible deniability stretched infinitesimally thin – and a knowing smirk on Putin's face.
  • (16) It is shown that the behavior of these waves may be explained, to a large extent, by considering the effect of the continuous stream of infinitesimal reflections that is set up whenever any wave travels in a region of vessel where the local impedance, (that is, the ratio of elastic wavespeed to tube area) is not constant.
  • (17) These changes could not be attributed to the effects of inbreeding or of selection in an infinitesimal model and suggested that some change in variance due to change in gene frequency had occurred during the course of the experiment.
  • (18) Ten healthy subjects received two treatments: a single 1 g oral dose of nalidixic acid (NA) followed 1 h later by either an infinitesimal dilution of the drug (NA 7CH) or by succussed water which served as placebo.
  • (19) The finite deformation theory describes the large strain behavior of cartilage observed in one-dimensional confined compression experiments at equilibrium, and it reduces to the linear biphasic theory under infinitesimal strain and slow strain rate conditions.
  • (20) Watson jokes that he has worked out that his Luton Town has an infinitesimally small chance of making it to the Premier League in time for matches to be aired on BT Vision before the end of the three-year deal in 2016.

Limit


Definition:

  • (v. t.) That which terminates, circumscribes, restrains, or confines; the bound, border, or edge; the utmost extent; as, the limit of a walk, of a town, of a country; the limits of human knowledge or endeavor.
  • (v. t.) The space or thing defined by limits.
  • (v. t.) That which terminates a period of time; hence, the period itself; the full time or extent.
  • (v. t.) A restriction; a check; a curb; a hindrance.
  • (v. t.) A determining feature; a distinguishing characteristic; a differentia.
  • (v. t.) A determinate quantity, to which a variable one continually approaches, and may differ from it by less than any given difference, but to which, under the law of variation, the variable can never become exactly equivalent.
  • (v. t.) To apply a limit to, or set a limit for; to terminate, circumscribe, or restrict, by a limit or limits; as, to limit the acreage of a crop; to limit the issue of paper money; to limit one's ambitions or aspirations; to limit the meaning of a word.
  • (v. i.) To beg, or to exercise functions, within a certain limited region; as, a limiting friar.

Example Sentences:

  • (1) Serum levels of both dihydralazine and metabolites were very low and particularly below the detection limit.
  • (2) This should not be a serious limitation to the application of the RIA in the detection of venous thrombosis.
  • (3) The rise of malaria despite of control measures involves several factors: the house spraying is no more accepted by a large percentage of house holders and the alternative larviciding has only a limited efficacy; the houses of American Indians have no walls to be sprayed; there is a continuous introduction of parasites by migrants.
  • (4) Increased infusion flow rate did not increase the limiting frequency.
  • (5) The extent of the infectious process was limited, however, because the life span of the cultures was not significantly shortened, the yields of infectious virus per immunofluorescent cell were at all times low, and most infected cells contained only a few well-delineated small masses of antigen, suggestive of an abortive infection.
  • (6) Limited biopsic retroperitoneal lymphnode dissection subsequently extended following the result of the frozen section histology.
  • (7) In addition, the fact that microheterogeneity may occur without limit in the mannans of the strains suggests that antibodies with unlimited diverse specificities are produced directed against these antigenic varieties as well.
  • (8) The specific limited trypsinolysis of bacteriophage T7 RNA polymerase (T7RP) was performed in the presence of various components of the polymerase reaction and some GTP-analogs--irreversible inhibitors of the enzyme.
  • (9) This postulate is supported by a limited study of the serovars present among the isolates.
  • (10) Breast reconstruction should not be limited to the requiring patients, but should represent, in selected cases with favourable prognosis, an integrative and complementary procedure of the treatment.
  • (11) As increases to the Isa allowance are based on the CPI inflation figure for the year to the previous September, the new data suggests the current Isa limit of £15,240 will remain unchanged next year.
  • (12) Conditions for limited digestion of the heterodimer by subtilisin, removing only the carboxyl terminus, were determined.
  • (13) Furthermore the limit between hearing aid fitting an cochlear implantation is discussed.
  • (14) Comprehensive regulations are being developed to limit human exposure to contamination in drinking water by the United States Environmental Protection Agency (EPA) under the authority of the Safe Drinking Water Act (SDWA).
  • (15) Direct limiting effects of hypothermia on tissue O2 delivery and muscle oxidative metabolism as well as vasoconstriction and arteriovenous shunting associated with CPB procedures are likely to be involved in the above mentioned alterations of cell metabolism.
  • (16) Their disadvantages - the expensive equipment and the time-consuming procedure respectively - limit their widespread use.
  • (17) The lower limit (LL) of CBF autoregulation was calculated by a computerized program and tested for different factors for correction of the PaCO2-induced changes in CBF.
  • (18) Immunochemical techniques, in particular ELISA are available for only a very limited number of NM (e.g.
  • (19) Only one E. coli strain, containing two plasmids that encode endo-pectate lyases, exo-pectate lyase, and endo-polygalacturonase, caused limited maceration.
  • (20) Initiation of the alternative pathway by the cryptococcal capsule is characterized by a lag in C3 accumulation and the appearance of a limited number of focal initiation sites which resemble those observed when the alternative pathway is activated by zymosan and nonencapsulated cryptococci.