What's the difference between infinite and infinitesimal?

Infinite


Definition:

  • (a.) Unlimited or boundless, in time or space; as, infinite duration or distance.
  • (a.) Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite.
  • (a.) Indefinitely large or extensive; great; vast; immense; gigantic; prodigious.
  • (a.) Greater than any assignable quantity of the same kind; -- said of certain quantities.
  • (a.) Capable of endless repetition; -- said of certain forms of the canon, called also perpetual fugues, so constructed that their ends lead to their beginnings, and the performance may be incessantly repeated.
  • (n.) That which is infinite; boundless space or duration; infinity; boundlessness.
  • (n.) An infinite quantity or magnitude.
  • (n.) An infinity; an incalculable or very great number.
  • (n.) The Infinite Being; God; the Almighty.

Example Sentences:

  • (1) Communicating sustainability is a subtle attempt at doing good Read more And yet, in environmental terms it is infinitely preferable to prevent waste altogether, rather than recycle it.
  • (2) After 14 days of storage the reduction factors were infinite, 30 and 5, respectively.
  • (3) The culture pattern presented by the primary cultures did not appreciably change after passaging in vitro for periods of up to 2 years, even after infinite cell lines were established.
  • (4) At infinite dilution both steroids are well resolved, the trans isomer being eluted before the cis isomer.
  • (5) However, the maximal lysis of target cells at an infinite number of effectors was significantly less for normal compared with leukaemic targets.
  • (6) But the character – compounded of piercing sanity and existential despair, infinite hesitation and impulsive action, self-laceration and observant irony – is so multi-faceted, it is bound to coincide at some point with an actor’s particular gifts.
  • (7) In this (proliferative) model small doses of weakly antigenic tumors grow infinitely large (i.e.
  • (8) The aim was to create an infinite number of ways in which the story could be read – though Pears emphasised that Arcadia was not an interactive novel.
  • (9) We have found that the frequency of the allele which favours recombination increases in finite populations, and decreases slightly in infinite populations.
  • (10) I believe there are infinite paths to accepting Jesus Christ as your personal saviour.
  • (11) Les Misérables is a game with destiny: it dramatises the gap between the imperfections of human judgments, and the perfect patterns of the infinite.
  • (12) The theoretical function described coherences between recording sites of small separation for linear, non-dispersive, dissipative waves moving on an infinite homogeneous plane medium, and driven by spatio-temporally noisy inputs.
  • (13) The changes in the integral of the extracellular action potentials (EAPs) generated by an infinite homogeneous fibre in an infinite homogeneous and isotropic volume conductor were studied at different radial distances (yo) from the fibre axis, depending on the propagation velocity (v), duration (Tin) and asymmetry of the intracellular action potential (IAP).
  • (14) The Macdonald-Dietz model for superinfection in malaria is a time-dependent infinite-server queue.
  • (15) The deterministic model (assuming infinite population size and random mating) predictions of the final gene frequency were exceeded only if there was reproductive compensation.
  • (16) Differential pencil beam (DPB) is defined as the dose distribution relative to the position of the first collision, per unit collision density, for a monoenergetic pencil beam of photons in an infinite homogeneous medium of unit density.
  • (17) Using fundamental concepts of hydrodynamics in porous media, we have rederived the Lumpkin-DèJardin-Zimm (LDZ) model for the gel electrophoresis of reptating, infinitely long, worm-like chains, such as DNA.
  • (18) Arthur Koestler in The Act of Creation expresses it thus: "From the Pythagoreans onward, through the Renaissance to our times, the oceanic feeling, the sense of participation in the mystery of the infinite, was the principal inspiration of the wingèd and flat-footed creature, the scientist."
  • (19) Pressure-volume curves from nine ferrets (including the above six) revealed almost infinitely compliant chest walls so that lung and total respiratory system curves were essentially the same.
  • (20) An orderly process of dealing with asylum claims at the earliest point would be infinitely preferable to desperate families laying siege to central European railway stations, risking their lives clinging on to vehicles at Calais or suffocating in vehicles transporting them across borders.

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.