What's the difference between infinitesimal and infinity?

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.

Infinity


Definition:

  • (n.) Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.
  • (n.) Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.
  • (n.) Endless or indefinite number; great multitude; as an infinity of beauties.
  • (n.) A quantity greater than any assignable quantity of the same kind.
  • (n.) That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.

Example Sentences:

  • (1) Multiple doses of cholestyramine significantly altered HCTZ kinetics, including reductions in Ae(0-24) by 35% (P less than 0.02), AUC(0-infinity) by 32% (P less than 0.01), and Cmax by 31% (P less than 0.01).
  • (2) The Infinity towel comes in colours more vibrant than one might expect from an eco-friendly product, including coral, green, blue and violet.
  • (3) In the interim, Gough had also played a devious old friend of the Doctor – by now, Peter Davison – in the 1983 story Arc of Infinity.
  • (4) The rate constants and steady-state values for m were in agreement with the Hodgkin-Huxley equations except that the experimental relationship of m(infinity) (3) against V was shifted 10-15 mV in the negative direction.
  • (5) 115 mM-TEA reduced the amplitude of [I(m)(0) - I(m)(infinity)] by about 85%.3.
  • (6) Some spoke of access to on-site rooftop infinity swimming pools and top of the range company cars.
  • (7) The final expression is mathematically accurate to 1% and is valid for image radii ranging from 20 to 500 mum and for exposure times from 30 ms to infinity.
  • (8) The data from the other 15 subjects showed small differences, which did not achieve statistical significance between the formulations with respect to Cmax, Tpeak and AUC0-infinity.
  • (9) We introduce the following functions of alpha m and beta m. (sequence in text) where VH, td and tau p stand for holding potential, constant delay time of 10 microseconds, and transit time of the transition velocity of alpha m (or beta m) from its initial value alpha om (or beta om) to its final steady value alpha infinity m (or beta infinity m), respectively.
  • (10) A second technician was arranged and claimed that BT often sells Infinity 2 for lines that can’t support the guaranteed speed.
  • (11) In adult myocytes, when EGTA (10 or 20 mM) or bis(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA, 10 mM) were included in the pipette solution, contractions were rapidly abolished, while a small (4 mV) shift of f infinity to more positive potentials was seen.
  • (12) By contrast, BT signed up 400,000 subscribers to its fibre product, Infinity, with 95,000 added in the last quarter.
  • (13) In the time-dependent transfer of a lipid from a donor to an acceptor vesicle population a(t) is the amount transferred to the acceptor vesicles at time t, a infinity is the equilibrium transfer value and a0 is the value at zero time.
  • (14) In the last quarter, 131,000 signed up for the BT Infinity fibre-to-the-cabinet product, which offers speeds of up to 76mbps and is being priced on a par with the fastest copper lines, meaning BT now has more than half a million fibre customers.
  • (15) We’re focusing on that right now with Infinity War while we’re breaking into those movies, [to see] which characters we can pull to the forefront who potentially haven’t had their own ‘A’ story arc to this point.
  • (16) After pulsed excitation with a polarized light, the fluorescence anisotropy ratio of DPH in membranes rapidly decreased and gave a final value (r infinity).
  • (17) The area under the plasma concentration-time curve from t = 0 to infinity (AUC infinity) of S(-)-mepivacaine was almost double that of R(+)-mepivacaine.
  • (18) From the results of intravenous injections one can deduce linear ibuprofen pharmacokinetics within the considered dosage range, with corresponding AUC0-infinity values of 3786 micrograms * min ml-1 and 7260 micrograms * min ml-1 for the 200 mg and 400 mg doses, respectively.
  • (19) The voltage dependence of the use-dependent block produced by cocaine isomers did not overlap with the activation of Na+ channels but did overlap with the steady-state inactivation (h infinity), indicating that cocaine can bind directly to the inactivated state of Na+ channels before channel opening.
  • (20) Following administration of 1000 mg MPA the areas under the plasma concentration-time curves (AUC 0-infinity) were calculated to (mean and S.E.