Not too great nor too small to be naturally susceptible of measurement, whether measurable by us or not; not infinite nor infinitesimal.The following are the special significations of the word: As applied to a class or integer number, capable of being completely counted: this is the fundamental meaning. This distinction between a finite and an infinite class is very important, because there is a peculiar mode of reasoning, called by logicians reasoning by transposed quantity, which is applicable to finite classes alone. The following syllogism is an example: “Every Hottentot kills a Hottentot; but no Hottentot is killed by more than one Hottentot; hence, every Hottentot is killed by a Hottentot.” If by the Hottentots is here meant a class of which a complete census might be taken, this conclusion must be true, provided the premises are true. But if the generations of Hottentots are everlasting, each Hottentot might kill one of his children, and yet some Hottentots might die natural deaths. Reasoning by transposed quantity is indispensable in the higher arithmetic and algebra; and consequently in these branches of mathematics the distinction between finite and infinite classes is very important.As applied to continuous quantity, smaller than a suitably chosen finite number multiplied into the unit of measurement, and larger than a suitably chosen finite number divided by the unit of measurement.In grammar, limited by person; personal; strictly verbal; not infinitival nor participial.Subject to limitations or conditions, such as those of space, time, circumstances, and the laws of nature: as, a finite being; finite existence or duration.Of or pertaining or relating to finite beings: as, finite passions or interests.In mathematics, an integral is said to be expressed in finite terms when it is expressed without resort to an infinite series, although it may be expressed by means of exponential, elliptic, or Abelian functions which are synonymous with infinite series; but frequently expressions involving higher kinds of functions than the exponential and trigonometric are excluded.n. That which is finite; finite things collectively: used only with the definite article.To limit; fix the limits of.
