calculus of finite differences
afmârik-e degarsânihâ-ye karânmand
Fr.: calcul des différences finies
A calculus based on the properties of the successive values of variable quantities and their differences or increments.
Clearly defined or determined; having fixed limits. → definite integral.
From L. definitus "limited, precise," p.p. of definire, → define.
Hedârmand from hedâr, stem of hedârdan, → define, + -mand possession suffix.
Fr.: intégrale définie
An integral with upper and lower limits.
1) Math: The opposite of → infinite.
From L. finitus, p.p. of finire "to limit, set bounds, end."
Karânmand, from karân "boundary, side, end, coast" + -mand adjective suffix. Karân, variants karâné, kenâr, from Mid.Pers. karân, karânak, kenâr "edge, limit, boundary," Av. karana- "side, boundary, end."
Fr.: population finie
A → statistical population consisting of individuals or items which are finite in number.
seri-ye karânmand (#)
Fr.: série finie
A sum a1 + a2 + a3 + · · · + aN, where the ai's are real numbers. In terms of Σ-notation, it is written as a1 + a2 + a3 + · · · + aN = Σ (n = 1 to N). See also → infinite series.
Fr.: ensemble fini
A → set whose elements can be numbered from 1 to n, for some positive integer n.
Not → definite; without fixed or specified limit.
Fr.: intégrale indéfinie
Math.: An integral without upper and lower limits. The general antiderivative of a function. → definite integral.
Unlimited or unmeasurable in extent of space, duration of time, etc.
Fr.: population infinie
A → statistical population consisting of individuals or items which either possesses the infinite property through some limiting process or is non-enumerable. For example, the population of all → real numbers between 0 and 1 and the population of all → integers are examples of infinite population. In case of random sampling with replacement, any population is always infinite.
seri-ye bikarân (#)
Fr.: série infinie
A series with infinitely many terms, in other words a series that has no last term, such as 1 + 1/4 + 1/9 + 1/16 + · · · + 1/n2 + ... . The idea of infinite series is familiar from decimal expansions, for instance the expansion π = 3.14159265358979... can be written as π = 3 + 1/10 + 4/102 + 1/103 + 5/104 + 9/105 + 2/106 + 6/107 + 5/108 + 3/109 + 5/1010 + 8/1011 + ... , so π is an "infinite sum" of fractions. See also → finite series.
Fr.: ensemble infini
A set which can be put in a one-to-one correspondence with part of itself.
General: Indefinitely or exceedingly small.
Infinitesimal, coined by Ger. philosopher and mathematician Baron Gottfried Wilhelm von Leibniz (1646-1716) from N.L. infinitesim(us) "infinite in rank," from infinit(us), → infinite, + -esimus suffix of ordinal numerals + → -al.
Bikarânxord, from bikarân "unbounded, unlimited, infinite," from bi- "without" + karân "boundary, side, end" (variants karâné, kenâr, from Mid.Pers. karân, karânak, kenâr "edge, limit, boundary," Av. karana- "side, boundary, end") + xord "minute, little, small" (from Mid.Pers. xvart, xôrt "small, insignificant;" Av. ādra- "weak, dependent;" Skt. ādhrá- "small, weak, poor," nādh "to be oppressed;" Gk. nothros "sluggish;" PIE base *nhdhro-).
Fr.: calcul infinitésimal
The body of rules and processes by means of which continuously varying magnitudes are dealt with in → calculus. The combined methods of mathematical analysis of → differential calculus and → integral calculus.