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.<\/p>\n
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.)<\/p>\n
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.)<\/p>\n
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.<\/p>\n
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).<\/p>\n
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.<\/p>\n
(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.<\/p>\n
* For LIMIT, in Heb 4:7<\/span>, AV, see DEFINE <\/p>\n 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 … Continue reading “Limit”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-62961","post","type-post","status-publish","format-standard","hentry","category-encyclopedic-dictionary"],"_links":{"self":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/posts\/62961","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/comments?post=62961"}],"version-history":[{"count":0,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/posts\/62961\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/media?parent=62961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/categories?post=62961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/tags?post=62961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Fuente: Vine’s Dictionary of New Testament Words<\/b><\/i><\/h4>\n","protected":false},"excerpt":{"rendered":"