infinite bikarân (#) Fr.: infini Unlimited or unmeasurable in extent of space, duration of time, etc. |
infinite population porineš-e bikarân 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. → infinite; → population. |
infinite series 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/n^{2} + ... . 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 + 4/10^{2} + 1/10^{3} + 5/10^{4} + 9/10^{5} + 2/10^{6} + 6/10^{7} + 5/10^{8} + 3/10^{9} + 5/10^{10} + 8/10^{11} + ... , so π is an "infinite sum" of fractions. See also → finite series. |
infinite set hangard-e bikarân Fr.: ensemble infini A set which can be put in a one-to-one correspondence with part of itself. |
infinitesimal bikarânxord Fr.: infinitésimal 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-). |
infinitesimal calculus afmârik-e bikarânxord 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. → infinitesimal, → calculus. |