What's the difference between finite and infinitesimal?

Finite


Definition:

  • (a.) Having a limit; limited in quantity, degree, or capacity; bounded; -- opposed to infinite; as, finite number; finite existence; a finite being; a finite mind; finite duration.

Example Sentences:

  • (1) According to the finite element analysis, the design bases of fixed restorations applied in the teeth accompanied with the absorption of the alveolar bone were preferred.
  • (2) The method is implemented with a digital non-causal (zero-phase shift) filter, based on the convolution with a finite impulse response, to make the computation time compatible with the use of low-cost microcomputers.
  • (3) The World Humanitarian Summit in May 2016 may be the most timely opportunity to make an honest appraisal of the effectiveness of the current system to deal with the sector’s “ new normal ” of finite resources and unlimited challenges.
  • (4) A model for left ventricular diastolic mechanics is formulated that takes into account noneligible wall thickness, incompressibility, finite deformation, nonlinear elastic effects, and the known fiber architecture of the ventricular wall.
  • (5) However, a region containing pixels that are perfectly synchronous on average would still yield a finite distribution of calculated Fourier coefficients due to the propagation of stochastic pixel noise into the calculated values.
  • (6) Linear phase finite impulse response (FIR) filtering can be used to differentiate auditory brainstem evoked potentials (ABEP) components.
  • (7) K5, an OKT8+ clone bearing multiple proviral integration sites, retained its HTLV-I-specific cytotoxicity and a normal dependence on interleukin 2 (IL-2), indicating that there is a finite number of transforming integration sites.
  • (8) Finite diffusivity in tissue and permeability restrictions can have significant effects on the proportion of the volume measured.
  • (9) The finite element algorithm is presented for the determination of heat flow within the partially frozen cornea during cryotherapy.
  • (10) As such, the finite size of the cellular membrane, as well as its precise symmetry, could not be incorporated into the previous studies.
  • (11) He is the embodiment of the belief that money and power provide a licence to impose one’s will on others, whether that entitlement is expressed by grabbing women or grabbing the finite resources from a planet on the verge of catastrophic warming.
  • (12) These particular observations illustrate that finite-amplitude distortion may be of considerable significance in the transmission through tissue of ultrasonic pulses during diagnostic scanning.
  • (13) A smooth isolated, axisymmetric occlusion in a straight vascular tube is a tractable problem for pulsatile flow calculations via finite-difference approximations to the Navier-Stokes equation.
  • (14) This paper presents a finite-difference method to calculate SAR in a realistic, heterogeneous model of the leg below the knee.
  • (15) Detailed analysis of microsphere distribution in a cubic centimeter of normal liver and the calculation of dose to a 3-dimensional fine grid has shown that the radiation distribution created by the finite size and distribution of the microspheres results in an highly heterogeneous dose pattern.
  • (16) Low-level finite state (locked-unlocked) control is compared with open-loop stimulation of the knee extensor muscles in functional electrical stimulation (FES) induced paraplegic standing.
  • (17) Thus a large portion of Rp binding to NAP may represent nonspecific binding rather than binding to a finite number of Rp acceptor sites.
  • (18) Biomechanical properties of the six major lumbar spine ligaments were determined from 38 fresh human cadaveric subjects for direct incorporation into mathematical and finite element models.
  • (19) The velocity field of the suspending fluid and the instantaneous velocities of the cylinders are computed by the finite element method.
  • (20) In addition, we studied facial morphology using finite-element scaling analysis and found that the two genera show similarities in morphological integration, or the way in which biological landmarks relate to one another in three dimensions to define the form of the organism.

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.