![The following is exactly what we mean by a LIMIT. ...let the several values of x... bea1 a2 a3 a4.... &c.;then if by passing from a1 to a2, from a2 to a3, &c.;, we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with an, and continuing ad infinitum,an an+1 an+2.... &c.;all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question. (Augustus De Morgan)](https://cdn.quotesdtb.com/img/quotes_images_webp/67/augustus-de-morgan-addition-533567.webp)
The following is exactly what we mean by a LIMIT. ...let the several values of x... bea1 a2 a3 a4.... &c.;then if by passing from a1 to a2, from a2 to a3, &c.;, we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with an, and continuing ad infinitum,an an+1 an+2.... &c.;all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question.
Augustus De MorganRelated topics
addition approach beginning case certain continuing differ following kind last less limit lower mean name passing quantity question respect say series set several small suppositionRelated quotes
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