remainder

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remainder

1. Maths
a. the amount left over when one quantity cannot be exactly divided by another
b. another name for difference
2. Property law a future interest in property; an interest in a particular estate that will pass to one at some future date, as on the death of the current possessor
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Remainder

The remainder in an approximation formula is the difference between the exact and the approximate values of the expression represented by the formula. A remainder can take different forms depending on the nature of the approximation formula. The task of investigating a remainder usually consists in obtaining estimates for it. For example, corresponding to the approximate formula we have the exact equality where the expression R is the remainder for the approximation 1.41 for the number and it is known that 0.004 < R < 0.005.

Remainders are constantly encountered in asymptotic formulas. For example, for the number π (x) of primes not exceeding x we have the asymptotic formula where μ is any positive number less than 3/5. Here, the remainder, which is the difference between the functions π (x) an ∫x2 du/ln u for x2, is written in the form

O[xe-(In x)μ

where the letter O indicates that the remainder does not exceed the expression

Cxe-(In x)μ

in absolute value, C being some positive constant. Remainders are found in formulas that give approximate representations of functions. For example, in the Taylor formula the remainder Rn (x) in Lagrange’s form is where θ is a number such that 0 < θ < 1; θ generally depends on the values of x and h. The presence of 0 in the formula for Rn(x) introduces an element of indefiniteness; such indefinite-ness is inherent in many formulas for the remainder.

Remainders also occur in quadrature formulas and interpolation formulas.

remainder

[ri′mān·dər]
(mathematics)
The remaining integer when a division of an integer by another is performed; if l = m · p + r, where l, m, p, and r are integers and r is less than p, then r is the remainder when l is divided by p.
The remaining polynomial when division of a polynomial is performed; if l = m · p + r, where l, m, p, and r are polynomials, and the degree of r is less than that of p, then r is the remainder when l is divided by p.
The remaining part of a convergent infinite series after a computation, for some n, of the first n terms.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

remainder

An interest in property that confers a right to possession in someone other than the grantor or his heirs upon the termination of a prior interest, such as following the death of a life tenant.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.
References in periodicals archive ?
-Remainder calculation function for easy division calculations to find a quotient and remainder
Marked by recurrent network imagery (mentions of wires, links, and grids abound) and discussions of financial speculation absent from the film, McCarthy's Remainder is about, among other things, quantification, abstraction, and the violence of applying computational models to a world marked by contingencies that will always exceed systematization.
The IRS issued a notice of deficiency, asserting that no deduction was allowed because the value of the charitable remainder interest did not equal at least 10% of the net FMV of the property contributed.
The valuation of excess land may require a different set of comparable sales from the remainder tract, and the group of potential purchasers may vary as well.
The income stream can be structured as a fixed dollar amount, as in the case of a charitable remainder annuity trust (CRAT), or as a percentage of the trust's annual fair market value, as in the case of a charitable remainder unitrust (CRUT).
In  Arhangel'skii studied properties of topological groups with an Ohio complete remainder. He proved that a non-locally compact topological group G has a remainder which is a p-space if and only if G is either a Lindelof p-space or a [sigma]-compact space.
The rules for calculating the present value of the remainder interest in a CRAT are in Regs.
On May 14, residents asked the workforce when they were starting work on the remainder of the road and were told that the remainder of the road was not being resurfaced.
The taxpayer-decedent in this case established a testamentary CLAT to benefit a private charitable foundation and the taxpayer's children as remainder beneficiaries.
Advice Follow for remainder of season Jackies Solitaire Anthony Honeyball 7th, Cheltenham, March 14 Her jumping was always fluent and she didn't really get the run of the race, but she made eyecatching headway in the home straight and should be suited by a greater test of stamina.
But, instead of writing a remainder of three, you would have written a fraction three fifths of a kilo, or a decimal 0.6kg or 600grams.

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