Limit
Limit
limit (, gebhul, bound): Occurs once in Eze 43:12 (limit of holy mountain). Limited (Psa 78:41) and limiteth (, horzo, Heb 4:7) are changed in the Revised Version (British and American) to provoked (the margin retains limited) and defineth respectively.
Fuente: International Standard Bible Encyclopedia
Limit
We give here only some of the most elementary mathematical senses of this word, in connection with real numbers. (Refer to the articles Number and Continuity.)
The limit of an infinite sequence of real numbers a1, a2, a3, . . . is said to be (the real number) b if for every positive real number e there is a positive integer N such that the difference between b and an is less than e whenever n is greater than N. (By the difference between b and an is here meant the non-negative difference, i.e., b-an if b is greater than an, an-b if b is less than an, and 0 if b is equal to an.)
Let f be a monadic function for which the range of the independent variable and the range of the dependent variable both consist of real numbers; let b and c be real numbers; and let g be the monadic function so determined that g(c)=b, and g(x)=f(x) if x is different from c. (The range of the independent variable for g is thus the same as that for f, with the addition of the real number c if not already included.) The limit of f(x) as x approaches c is said to be b if g is continuous at c. — More briefly but less accurately, the limit of f(x) as x approaches c is the value which rrust be assigned to f for the argument c in order to make it continuous at c.
The limit of f(x) as x approaches infinity is said to be b, if the limit of h(x) as x approaches 0 is b, where h is the function so determined that h(x)=f( 1/x).
In connection with the infinite sequence of real numbers a1, a2, a3 . . ., a monadic function a may be introduced for which the range of the independent variable consists of the positive integers 1, 2, 3, . . . and a(1)=a1, a(2)=a2, a(3)=a3, . . . . It can then be shown that the limit of the infinite sequence as above defined is the same as the limit of a(x) as x approaches infinity.
(Of course it is not meant to be implied in the preceding that the limit of an infinite sequence or of a function always exists. In particular cases it may happen that there is no limit of an infinite sequence, or no limit of f(x) as x approaches c, etc.) — A.C.
Fuente: The Dictionary of Philosophy
Limit
* For LIMIT, in Heb 4:7, AV, see DEFINE