What's the difference between infinitesimal and small?

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.

Small


Definition:

  • (superl.) Having little size, compared with other things of the same kind; little in quantity or degree; diminutive; not large or extended in dimension; not great; not much; inconsiderable; as, a small man; a small river.
  • (superl.) Being of slight consequence; feeble in influence or importance; unimportant; trivial; insignificant; as, a small fault; a small business.
  • (superl.) Envincing little worth or ability; not large-minded; -- sometimes, in reproach, paltry; mean.
  • (superl.) Not prolonged in duration; not extended in time; short; as, after a small space.
  • (superl.) Weak; slender; fine; gentle; soft; not loud.
  • (adv.) In or to small extent, quantity, or degree; little; slightly.
  • (adv.) Not loudly; faintly; timidly.
  • (n.) The small or slender part of a thing; as, the small of the leg or of the back.
  • (n.) Smallclothes.
  • (n.) Same as Little go. See under Little, a.
  • (v. t.) To make little or less.

Example Sentences:

  • (1) The effect of insulin-like growth factor I (IGF-I) on growth of small cell lung cancer (SCLC) cell lines was studied.
  • (2) Such a signal must be due to a small ferromagnetic crystal formed when the nerve is subjected to pressure, such as that due to mechanical injury.
  • (3) The Na+ ionophore, gramicidin, had a small but significant inhibitory effect on Na(+)-dependent KG uptake, demonstrating that KG uptake was not the result of an intravesicular positive Na+ diffusion potential.
  • (4) For some time now, public opinion polls have revealed Americans' strong preference to live in comparatively small cities, towns, and rural areas rather than in large cities.
  • (5) The predicted non-Lorentzian line shapes and widths were found to be in good agreement with experimental results, indicating that the local orientational order (called "packing" by many workers) in the bilayers of small vesicles and in multilamellar membranes is substantially the same.
  • (6) If Charles Spencer, 3rd Duke of Marlborough, who bought the island in 1738, were to return today he would doubtless recognise the scene, though he might be surprised that his small private buildings have grown into a sizable hotel.
  • (7) We conclude that chronic emphysema produced in dogs by aerosol administration of papain results in elevated pulmonary artery pressure, which is characterized pathologically by medial hypertrophy of small pulmonary arteries.
  • (8) As the percentage of rabbit feed is very small compared to the bulk of animal feeds, there is a fair chance that rabbit feed will be contaminated with constituents (additives) of batches previously prepared for other animals.
  • (9) 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.
  • (10) The small units described here could be inhibitory interneurons which convert the excitatory response of large units into inhibition.
  • (11) Early stabilisation may not ensure normal development but even early splinting carries a small risk of avascular necrosis.
  • (12) Twenty patients with non-small cell bronchogenic carcinoma were prospectively studied for intrathoracic lymphadenopathy using computed tomography (CT) and magnetic resonance imaging (MRI).
  • (13) In addition, KM231 could detect a small amount of the antigen ganglioside in human gastric normal and cancerous mucosa and in gastric cancer cell lines by HPTLC-immunostaining.
  • (14) Two small populations of GLY + neurons were observed outside of the named nuclei of the SOC; one was located dorsal to the LSO, near its dorsal hilus, and the other was identified near the medial pole of the LSO.
  • (15) Because of the small number of patients reported in the world literature and lack of controlled studies, the treatment of small cell carcinoma of the larynx remains controversial; this retrospective analysis suggests that combination chemotherapy plus radiation offers the best chance for cure.
  • (16) Only small amounts of 3H oleic acid were converted.
  • (17) The pH gradient measured with dimethyloxazolidine-2,4-dione and acetylsalicylic acid was very small in both bacteria at a high pH above 8, and was not affected significantly by the addition of CCCP.
  • (18) The results also indicate that small lesions initially noted only on CT scans of the chest in children with Wilms' tumor frequently represent metastatic tumor.
  • (19) CT scan revealed a small calcified mass in the right maxillary sinus.
  • (20) We have previously shown that intratracheally instilled silica (quartz) produces both morphologic evidence of emphysema and small-airway changes, and functional evidence of airflow obstruction.